Version 5.50.1318
The Mizar Mathematical Library Catalogue
========================================
(C) Copyright 1989-2018 Association of Mizar Users
I. Axiomatics
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1. HIDDEN
Built-in Concepts
by Andrzej Trybulec
Received January 1, 1989
2. TARSKI_0
Axioms of Tarski Grothendieck Set Theory
by Andrzej Trybulec
Received January 1, 1989
3. TARSKI_A
Tarski Grothendieck Set Theory -- Tarski's Axiom A
by Andrzej Trybulec
Received January 1, 1989
II. Addenda
-------
1. AXIOMS
Strong arithmetic of real numbers
by Andrzej Trybulec
Received January 1, 1989
2. STRUCT_0
Preliminaries to Structures
by Library Committee
Received January 6, 1995
3. ARYTM
Preliminaries to Arithmetic
by Library Committee
Received December 10, 1995
Has been removed on February 11, 2003
4. ARYTM_3
Arithmetic of Non Negative Rational Numbers
by Grzegorz Bancerek
Received March 7, 1998
5. ARYTM_2
Non negative real numbers. Part I
by Andrzej Trybulec
Received March 7, 1998
6. ARYTM_1
Non negative real numbers. Part II
by Andrzej Trybulec
Received March 7, 1998
7. ARYTM_0
Introduction to Arithmetic
by Andrzej Trybulec
Received January 9, 2003
8. NUMBERS
Subsets of Complex Numbers
by Andrzej Trybulec
Received November 7, 2003
9. BINOP_2
Binary Operations on Numbers
by Library Committee
Received June 21, 2004
10.NAT_D
Divisibility of Natural Numbers
by Grzegorz Bancerek
Received January 3, 2007
11.VALUED_0
Number-valued Functions
by Library Committee
Received November 22, 2007
12.ALGSTR_0
Basic Algebraic Structures
by Library Committee
Received December 8, 2007
13.VALUED_1
Properties of Number-valued Functions
by Library Committee
Received December 18, 2007
14.SCMNORM
Normal Computers
by Andrzej Trybulec
Received March 3, 2008
Has been removed on May 20, 2010
15.PRE_POLY
Preliminaries to Polynomials
by Andrzej Trybulec
Received August 7, 2009
16.NORMSP_0
Preliminaries to Normed Spaces
by Andrzej Trybulec
Received March 23, 2010
17.AMI_WSTD
Weakly Standard Ordering of Instruction Locations
by Andrzej Trybulec , Piotr Rudnicki and Artur Korni{\l}owicz
Received April 22, 2010
18.COMPOS_1
Composition of Machines, Instructions and Programs
by Andrzej Trybulec
Received May 20, 2010
19.EXTPRO_1
Externally Programmed Machines
by Yatsuka Nakamura and Andrzej Trybulec
Received June 30, 2010
20.AMISTD_5
Relocable Instructions
by Andrzej Trybulec
Received November 20, 2010
21.MEMSTR_0
Memory Structures
by Andrzej Trybulec
Received April 28, 2011
22.KURATO_0
On the {K}uratowski Limit Operators, I
by Adam Grabowski
Extracted from KURATO_2 on May 30, 2011
23.PARTFUN4
On the Real Valued Functions
by Artur Korni{\l}owicz
Extracted from PARTFUN3 on May 30, 2011
24.COMPOS_0
Commands Structure
by Andrzej Trybulec
Received May 20, 2010
25.SCM_INST
On a Mathematical Model of Programs -- Preliminaries
by Yatsuka Nakamura and Andrzej Trybulec
Received December 29, 1992
Extracted from AMI_2, 2012
26.SCMFSA_I
The Instructions for SCM+FSA Computer
by Andrzej Trybulec , Yatsuka Nakamura and Piotr Rudnicki
Received February 3, 1996
Extracted from SCMFSA_1, 2012
27.SCMRINGI
The Construction of { \bf SCM } over Ring -- Preliminaries
by Artur Korni{\l}owicz
Received November 29, 1998
Extracted from SCMRING1, 2012
28.SCMPDS_I
The Instructions for the SCMPDS Computer
by JingChao Chen
Received June 15, 1999
Extracted from SCPDS_1, 2012
29.SCMFSA_M
On the memory of SCM+FSA
by Library Committee
Received October 1, 2011
30.COMPOS_2
The Elementary Macroinstructions
by Andrzej Trybulec
Received October 1, 2011
31.MATRIX_0
Matrices
by Katarzyna Jankowska
Received June 8, 1991
Extracted from MATRIX_1, 2012
32.SCMFSA_X
On SCM+FSA Programs
by Andrzej Trybulec
Received May 19, 2013
33. TARSKI
Tarski Grothendieck Set Theory
by Andrzej Trybulec
Received January 1, 1989
Moved from Axiomatics section as now it can be proved based on TARSKI_0
III. Requirements files
------------------
1. BOOLE
Boolean Properties of Sets - Requirements
by Library Committee
Received April 30, 2002
2. SUBSET
Basic Properties of Subsets - Requirements
by Library Committee
Received February 27, 2003
3. NUMERALS
Numerals - Requirements
by Library Committee
Received February 27, 2003
4. REAL
Basic Properties of Real Numbers - Requirements
by Library Committee
Received February 27, 2003
5. ARITHM
Field Properties of Complex Numbers - Requirements
by Library Committee
Received May 29, 2003
IV. EMM - Encyclopedia of Mathematics in Mizar
-------------------------------------------
1. XBOOLE_0
Boolean Properties of Sets - Definitions
by Library Committee
Received April 6, 2002
2. XBOOLE_1
Boolean Properties of Sets - Theorems
by Library Committee
Received April 8, 2002
3. XREAL_0
Introduction to Arithmetic of Real Numbers
by Library Committee
Received February 11, 2003
4. XCMPLX_0
Complex Numbers - Basic Definitions
by Library Committee
Received March 7, 2003
5. XCMPLX_1
Complex Numbers - Basic Theorems
by Library Committee
Received April 10, 2003
6. XREAL_1
Real Numbers - Basic Theorems
by Library Committee
Received February 9, 2005
7. XXREAL_0
Introduction to Arithmetic of Extended Real Numbers
by Library Committee
Received January 4, 2006
8. XBOOLEAN
On the Arithmetic of Boolean Values
by Library Committee
Received November 30, 2006
9. XXREAL_1
Basic Properties of Extended Real Numbers
by Andrzej Trybulec, Yatsuka Nakamura, Artur Korni{\l}owicz and
Adam Grabowski
Received January 22, 2007
10.XXREAL_2
Suprema and Infima of Intervals of Extended Real Numbers
by Andrzej Trybulec
Received June 26, 2008
11.XXREAL_3
Basic Operations on Extended Real Numbers
by Andrzej Trybulec
Received September 23, 2008
12.XTUPLE_0
Kuratowski Pairs. Tuples and Projections
by Grzegorz Bancerek, Artur Korni\l owicz and Andrzej Trybulec
Received December 9, 2011
13.XREGULAR
Consequences of Regularity Axiom
by Andrzej Trybulec
Received January 30, 2012
14.XFAMILY
Families of Subsets
by Andrzej Trybulec
Received December 13, 2012
V. MML Articles
------------
1. BOOLE
Boolean Properties of Sets
by Zinaida Trybulec and Halina \'Swi\c{e}czkowska
Received January 6, 1989
Has been removed on April 10, 2002
2. ENUMSET1
Enumerated Sets
by Andrzej Trybulec
Received January 8, 1989
3. REAL_1
Basic Properties of Real Numbers
by Krzysztof Hryniewiecki
Received January 8, 1989
4. NAT_1
The Fundamental Properties of Natural Numbers
by Grzegorz Bancerek
Received January 11, 1989
5. ZFMISC_1
Some Basic Properties of Sets
by Czes{\l}aw Byli\'nski
Received February 1, 1989
6. FUNCT_1
Functions and Their Basic Properties
by Czes{\l}aw Byli\'nski
Received March 3, 1989
7. SUBSET_1
Properties of Subsets
by Zinaida Trybulec
Received March 4, 1989
8. RELAT_1
Relations and Their Basic Properties
by Edmund Woronowicz
Received March 15, 1989
9. RELAT_2
Properties of Binary Relations
by Edmund Woronowicz and Anna Zalewska
Received March 15, 1989
10. ORDINAL1
The Ordinal Numbers. Transfinite Induction and Defining by
Transfinite Induction
by Grzegorz Bancerek
Received March 20, 1989
11. MCART_1
Tuples, Projections and Cartesian Products
by Andrzej Trybulec
Received March 30, 1989
12. FINSEQ_1
Segments of Natural Numbers and Finite Sequences
by Grzegorz Bancerek and Krzysztof Hryniewiecki
Received April 1, 1989
13. DOMAIN_1
Domains and Their Cartesian Products
by Andrzej Trybulec
Received April 3, 1989
14. WELLORD1
The Well Ordering Relations
by Grzegorz Bancerek
Received April 4, 1989
15. ZF_LANG
A Model of ZF Set Theory Language
by Grzegorz Bancerek
Received April 4, 1989
16. SETFAM_1
Families of Sets
by Beata Padlewska
Received April 5, 1989
17. FUNCT_2
Functions from a Set to a Set
by Czes{\l}aw Byli\'nski
Received April 6, 1989
18. FINSET_1
Finite Sets
by Agata Darmochwa\l
Received April 6, 1989
19. GRFUNC_1
Graphs of Functions
by Czes{\l}aw Byli\'nski
Received April 14, 1989
20. BINOP_1
Binary Operations
by Czes{\l}aw Byli\'nski
Received April 14, 1989
21. RELSET_1
Relations Defined on Sets
by Edmund Woronowicz
Received April 14, 1989
22. FINSUB_1
Boolean Domains
by Andrzej Trybulec and Agata Darmochwa\l
Received April 14, 1989
23. ZF_MODEL
Models and Satisfiability. Defining by Structural Induction and
Free Variables in ZF-formulae
by Grzegorz Bancerek
Received April 14, 1989
24. ZF_COLLA
The Contraction Lemma
by Grzegorz Bancerek
Received April 14, 1989
25. INCSP_1
Axioms of Incidence
by Wojciech A. Trybulec
Received April 14, 1989
26. LATTICES
Introduction to Lattice Theory
by Stanis{\l}aw \.Zukowski
Received April 14, 1989
27. PRE_TOPC
Topological Spaces and Continuous Functions
by Beata Padlewska and Agata Darmochwa\l
Received April 14, 1989
28. TOPS_1
Subsets of Topological Spaces
by Miros{\l}aw Wysocki and Agata Darmochwa\l
Received April 28, 1989
29. CONNSP_1
Connected Spaces
by Beata Padlewska
Received May 6, 1989
30. FUNCT_3
Basic Functions and Operations on Functions
by Czes{\l}aw Byli\'nski
Received May 9, 1989
31. TOPS_2
Families of Subsets, Subspaces and Mappings in Topological Spaces
by Agata Darmochwa{\l}
Received June 21, 1989
32. ABSVALUE
Some Properties of Functions Modul and Signum
by Jan Popio{\l}ek
Received June 21, 1989
33. WELLORD2
Zermelo Theorem and Axiom of Choice. The correspondence of
well ordering relations and ordinal numbers
by Grzegorz Bancerek
Received June 26, 1989
34. SEQ_1
Real Sequences and Basic Operations on Them
by Jaros{\l}aw Kotowicz
Received July 4, 1989
35. SEQ_2
Convergent Sequences and the Limit of Sequences
by Jaros{\l}aw Kotowicz
Received July 4, 1989
36. ZFMODEL1
Properties of ZF Models
by Grzegorz Bancerek
Received July 5, 1989
37. ORDINAL2
Sequences of Ordinal Numbers. Beginnings of Ordinal Arithmetics
by Grzegorz Bancerek
Received July 18, 1989
38. RLVECT_1
Vectors in Real Linear Space
by Wojciech A. Trybulec
Received July 24, 1989
39. RLSUB_1
Subspaces and Cosets of Subspaces in Real Linear Space
by Wojciech A. Trybulec
Received July 24, 1989
40. QC_LANG1
A First Order Language
by Piotr Rudnicki and Andrzej Trybulec
Received August 8, 1989
41. ORDERS_1
Partially Ordered Sets
by Wojciech A. Trybulec
Received August 30, 1989
42. RECDEF_1
Recursive Definitions
by Krzysztof Hryniewiecki
Received September 4, 1989
43. FUNCOP_1
Binary Operations Applied to Functions
by Andrzej Trybulec
Received September 4, 1989
44. VECTSP_1
Abelian Groups, Fields and Vector Spaces
by Eugeniusz Kusak, Wojciech Leo\'nczuk and Micha{\l} Muzalewski
Received November 23, 1989
45. PARSP_1
Parallelity Spaces
by Eugeniusz Kusak, Wojciech Leo\'nczuk and Micha{\l} Muzalewski
Received November 23, 1989
46. SYMSP_1
Construction of a bilinear antisymmetric form in symplectic vector space
by Eugeniusz Kusak, Wojciech Leo\'nczuk and Micha{\l} Muzalewski
Received November 23, 1989
47. ORTSP_1
Construction of a bilinear symmetric form in orthogonal vector space
by Eugeniusz Kusak, Wojciech Leo\'nczuk and Micha{\l} Muzalewski
Received November 23, 1989
48. PARTFUN1
Partial Functions
by Czes{\l}aw Byli\'nski
Received September 18, 1989
49. SETWISEO
Semilattice Operations on Finite Subsets
by Andrzej Trybulec
Received September 18, 1989
50. CARD_1
Cardinal Numbers
by Grzegorz Bancerek
Received September 19, 1989
51. COMPTS_1
Compact Spaces
by Agata Darmochwa{\l}
Received September 19, 1989
52. ORDERS_2
Kuratowski - Zorn Lemma
by Wojciech A. Trybulec and Grzegorz Bancerek
Received September 19, 1989
53. RLSUB_2
Operations on Subspaces in Real Linear Space
by Wojciech A. Trybulec
Received September 20, 1989
54. PROB_1
$\sigma$-Fields and Probability
by Andrzej N\c{e}dzusiak
Received October 16, 1989
55. CAT_1
Introduction to Categories and Functors
by Czes{\l}aw Byli\'nski
Received October 25, 1989
56. TREES_1
Introduction to Trees
by Grzegorz Bancerek
Received October 25, 1989
57. WELLSET1
Zermelo's Theorem
by Bogdan Nowak and S{\l}awomir Bia{\l}ecki
Received October 27, 1989
58. REALSET1
Group and Field Definitions
by J\'ozef Bia{\l}as
Received October 27, 1989
59. EQREL_1
Equivalence Relations and Classes of Abstraction
by Konrad Raczkowski and Pawe{\l} Sadowski
Received November 16, 1989
60. SQUARE_1
Some Properties of Real Numbers.
Operations: min, max, square, and square root
by Andrzej Trybulec and Czes{\l}aw Byli\'nski
Received November 16, 1989
61. QC_LANG2
Connectives and Subformulae of the First Order Language
by Grzegorz Bancerek
Received November 23, 1989
62. QC_LANG3
Variables in Formulae of the First Order Language
by Czes{\l}aw Byli\'nski and Grzegorz Bancerek
Received November 23, 1989
63. SEQM_3
Monotone Real Sequences. Subsequences
by Jaros{\l}aw Kotowicz
Received November 23, 1989
64. SEQ_4
Convergent Real Sequences. Upper and Lower Bound of Sets of Real Numbers
by Jaros{\l}aw Kotowicz
Received November 23, 1989
65. MIDSP_1
Midpoint algebras
by Micha{\l} Muzalewski
Received November 26, 1989
66. QMAX_1
The Fundamental Logic Structure in Quantum Mechanics
by Pawe{\l} Sadowski, Andrzej Trybulec and Konrad Raczkowski
Received December 18, 1989
67. FRAENKEL
Function Domains and Fr{\ae}nkel Operator
by Andrzej Trybulec
Received February 7, 1990
68. INT_1
Integers
by Micha{\l} J. Trybulec
Received February 7, 1990
69. COMPLEX1
The Complex Numbers
by Czes{\l}aw Byli\'nski
Received March 1, 1990
70. ORDINAL3
Ordinal Arithmetics
by Grzegorz Bancerek
Received March 1, 1990
71. FUNCT_4
The Modification of a Function by a Function
and the Iteration of the Composition of a Function
by Czes{\l}aw Byli\'nski
Received March 1, 1990
72. FINSEQ_2
Finite Sequences and Tuples of Elements of a Non-empty Sets
by Czes{\l}aw Byli\'nski
Received March 1, 1990
73. FUNCT_5
Curried and Uncurried Functions
by Grzegorz Bancerek
Received March 6, 1990
74. CARD_2
Cardinal Arithmetics
by Grzegorz Bancerek
Received March 6, 1990
75. PARSP_2
Fano-Desargues Parallelity Spaces
by Eugeniusz Kusak and Wojciech Leo\'nczuk
Received March 23, 1990
76. FUNCSDOM
Real Functions Spaces
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
Received March 23, 1990
77. CLASSES1
Tarski's Classes and Ranks
by Grzegorz Bancerek
Received March 23, 1990
78. FINSEQ_3
Non-contiguous Substrings and One-to-one Finite Sequences
by Wojciech A. Trybulec
Received April 8, 1990
79. FINSEQ_4
Pigeon Hole Principle
by Wojciech A. Trybulec
Received April 8, 1990
80. RLVECT_2
Linear Combinations in Real Linear Space
by Wojciech A. Trybulec
Received April 8, 1990
81. CARD_3
K\"onig's Theorem
by Grzegorz Bancerek
Received April 10, 1990
82. CLASSES2
Universal Classes
by Bogdan Nowak and Grzegorz Bancerek
Received April 10, 1990
83. ANALOAF
Analytical Ordered Affine Spaces
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
Received April 11, 1990
84. METRIC_1
Metric Spaces
by Stanis{\l}awa Kanas, Adam Lecko and Mariusz Startek
Received May 3, 1990
85. DIRAF
Ordered Affine Spaces Defined in Terms of Directed Parallelity - part I
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
Received May 4, 1990
86. AFF_1
Parallelity and Lines in Affine Spaces
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
Received May 4, 1990
87. AFF_2
Classical Configurations in Affine Planes
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
Received April 13, 1990
88. AFF_3
Affine Localizations of Desargues Axiom
by Eugeniusz Kusak, Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
Received April 26, 1990
89. FINSEQOP
Binary Operations Applied to Finite Sequences
by Czes{\l}aw Byli\'nski
Received May 4, 1990
90. SETWOP_2
Semigroup operations on finite subsets
by Czes{\l}aw Byli\'nski
Received May 4, 1990
91. COLLSP
The Collinearity Structure
by Wojciech Skaba
Received May 9, 1990
92. RVSUM_1
The Sum and Product of Finite Sequences of Real Numbers
by Czes{\l}aw Byli\'nski
Received May 11, 1990
93. CQC_LANG
A Classical First Order Language
by Czes{\l}aw Byli\'nski
Received May 11, 1990
94. PASCH
Classical and Non--classical Pasch Configurations in Ordered Affine Planes
by Henryk Oryszczyszyn, Krzysztof Pra\.zmowski and
Ma{\l}gorzata Pra\.zmowska
Received May 16, 1990
95. REAL_LAT
The Lattice of Real Numbers. The Lattice of Real Functions
by Marek Chmur
Received May 22, 1990
96. TDGROUP
A Construction of an Abstract Space of Congruence of Vectors
by Grzegorz Lewandowski and Krzysztof Pra\.zmowski
Received May 23, 1990
97. CQC_THE1
A First-Order Predicate Calculus.
Axiomatics, the Consequence Operation and a Concept of Proof
by Agata Darmochwa{\l}
Received May 25, 1990
98. PARTFUN2
Partial Functions from a Domain to a Domain
by Jaros{\l}aw Kotowicz
Received May 31, 1990
99. RFUNCT_1
Partial Functions from a Domain to the Set of Real Numbers
by Jaros{\l}aw Kotowicz
Received May 27, 1990
100. ORDINAL4
Increasing and Continuous Ordinal Sequences
by Grzegorz Bancerek
Received May 31, 1990
101. TRANSGEO
Transformations in Affine Spaces
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
Received May 31, 1990
102. CAT_2
Subcategories and Products of Categories
by Czes{\l}aw Byli\'nski
Received May 31, 1990
103. MARGREL1
Many-Argument Relations
by Edmund Woronowicz
Received June 1, 1990
104. VALUAT_1
Interpretation and Satisfiability in the First Order Logic
by Edmund Woronowicz
Received June 1, 1990
105. PROB_2
Probability. Independence of Events and Conditional Probability
by Andrzej N\c{e}dzusiak
Received June 1, 1990
106. TRANSLAC
Translations in Affine Planes
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
Received June 12, 1990
107. RPR_1
Introduction to Probability
by Jan Popio{\l}ek
Received June 13, 1990
108. ANPROJ_1
A Construction of Analytical Projective Space
by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
Received June 15, 1990
109. ANPROJ_2
Projective Spaces - Part I
by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
Received June 15, 1990
110. RCOMP_1
Topological Properties of Subsets in Real Numbers
by Konrad Raczkowski and Pawe{\l} Sadowski
Received June 18, 1990
111. RFUNCT_2
Properties of Real Functions
by Jaros{\l}aw Kotowicz
Received June 18, 1990
112. FCONT_1
Real Function Continuity
by Konrad Raczkowski and Pawe{\l} Sadowski
Received June 18, 1990
113. FCONT_2
Real Function Uniform Continuity
by Jaros{\l}aw Kotowicz and Konrad Raczkowski
Received June 18, 1990
114. FDIFF_1
Real Function Differentiability
by Konrad Raczkowski and Pawe{\l} Sadowski
Received June 18, 1990
115. ROLLE
Average Value Theorems for Real Functions of One Variable
by Jaros{\l}aw Kotowicz, Konrad Raczkowski and Pawe{\l} Sadowski
Received June 18, 1990
116. VECTSP_2
Construction of Rings and Left-, Right-, and Bi-Modules over a Ring
by Micha{\l} Muzalewski
Received June 20, 1990
117. REALSET2
Properties of Fields
by J\'ozef Bia{\l}as
Received June 20, 1990
118. FILTER_0
Filters - Part I. Implicative Lattices
by Grzegorz Bancerek
Received July 3, 1990
119. GROUP_1
Groups
by Wojciech A. Trybulec
Received July 3, 1990
120. INT_2
The Divisibility of Integers and Integer Relatively Primes
by Rafa{\l} Kwiatek and Grzegorz Zwara
Received July 10, 1990
121. ALGSTR_1
From Loops to Abelian Multiplicative Groups with Zero
by Micha{\l} Muzalewski and Wojciech Skaba
Received July 10, 1990
122. RAT_1
Basic Properties of Rational Numbers
by Andrzej Kondracki
Received July 10, 1990
123. RLVECT_3
Basis of Real Linear Space
by Wojciech A. Trybulec
Received July 10, 1990
124. VECTSP_3
Finite Sums of Vectors in Vector Space
by Wojciech A. Trybulec
Received July 12, 1990
Has been removed on June 30, 2010
125. GROUP_2
Subgroup and Cosets of Subgroups. Lagrange theorem
by Wojciech A. Trybulec
Received July 23, 1990
126. VECTSP_4
Subspaces and Cosets of Subspaces in Vector Space
by Wojciech A. Trybulec
Received July 27, 1990
127. VECTSP_5
Operations on Subspaces in Vector Space
by Wojciech A. Trybulec
Received July 27, 1990
128. VECTSP_6
Linear Combinations in Vector Space
by Wojciech A. Trybulec
Received July 27, 1990
129. VECTSP_7
Basis of Vector Space
by Wojciech A. Trybulec
Received July 27, 1990
130. NEWTON
Factorial and Newton coeffitients
by Rafa{\l} Kwiatek
Received July 27, 1990
131. ANALMETR
Analytical Metric Affine Spaces and Planes
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
Received August 10, 1990
132. ANPROJ_3
Projective Spaces - part II
by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
Received August 10, 1990
Has been removed on March 7, 1995
133. ANPROJ_4
Projective Spaces - part III
by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
Received August 10, 1990
Has been removed on March 7, 1995
134. ANPROJ_5
Projective Spaces - part IV
by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
Received August 10, 1990
Has been removed on March 7, 1995
135. ANPROJ_6
Projective Spaces - part V
by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
Received August 10, 1990
Has been removed on March 7, 1995
136. ANPROJ_7
Projective Spaces - part VI
by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
Received August 10, 1990
Has been removed on March 7, 1995
137. NET_1
Some Elementary Notions of the Theory of Petri Nets
by Waldemar Korczy\'nski
Received August 10, 1990
138. GROUP_3
Classes of Conjugation. Normal Subgroups
by Wojciech A. Trybulec
Received August 10, 1990
139. ZF_LANG1
Replacing of Variables in Formulas of ZF Theory
by Grzegorz Bancerek
Received August 10, 1990
140. ZF_REFLE
The Reflection Theorem
by Grzegorz Bancerek
Received August 10, 1990
141. FINSOP_1
Binary Operations on Finite Sequences
by Wojciech A. Trybulec
Received August 10, 1990
142. LATTICE2
Finite Join and Finite Meet, and Dual Lattices
by Andrzej Trybulec
Received August 10, 1990
143. ZFREFLE1
Consequences of the Reflection Theorem
by Grzegorz Bancerek
Received August 13, 1990
144. PROJDES1
Desargues Theorem In Projective 3-Space
by Eugeniusz Kusak
Received August 13, 1990
145. LIMFUNC1
The Limit of a Real Function at Infinity. Halflines.
Real Sequence Divergent to Infinity
by Jaros{\l}aw Kotowicz
Received August 20, 1990
146. LIMFUNC2
One-Side Limits of a Real Function at a Point
by Jaros{\l}aw Kotowicz
Received August 20, 1990
147. GROUP_4
Lattice of Subgroups of a Group. Frattini Subgroup
by Wojciech A. Trybulec
Received August 22, 1990
148. REAL_2
Equalities and Inequalities in Real Numbers. Continuation of Real_1
by Andrzej Kondracki
Received September 5, 1990
Has been removed on December 19, 2008
149. CARD_4
Countable Sets and Hessenberg's Theorem
by Grzegorz Bancerek
Received September 5, 1990
150. LIMFUNC3
The Limit of a Real Function at a Point
by Jaros{\l}aw Kotowicz
Received September 5, 1990
151. LIMFUNC4
The Limit of a Composition of Real Functions
by Jaros{\l}aw Kotowicz
Received September 5, 1990
152. CONNSP_2
Locally Connected Spaces
by Beata Padlewska
Received September 5, 1990
153. ALGSEQ_1
Construction of Finite Sequences over Ring and Left-, Right-,
and Bi-Modules over a Ring
by Micha{\l} Muzalewski and Les{\l}aw W. Szczerba
Received September 13, 1990
154. TOLER_1
Relations of Tolerance
by Krzysztof Hryniewiecki
Received September 20, 1990
155. NORMSP_1
Real Normed Space
by Jan Popio{\l}ek
Received September 20, 1990
156. SCHEME1
Schemes of Existence of some Types of Functions
by Jaros{\l}aw Kotowicz
Received September 21, 1990
157. PREPOWER
Integer and Rational Exponents
by Konrad Raczkowski
Received September 21, 1990
158. HOMOTHET
Homotheties and Shears in Affine Planes
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
Received September 21, 1990
159. AFVECT0
Directed Geometrical Bundles and Their Analytical Representation
by Grzegorz Lewandowski, Krzysztof Pra\.zmowski and Bo\.zena Lewandowska
Received September 24, 1990
160. ZFMODEL2
Definable Functions
by Grzegorz Bancerek
Received September 26, 1990
161. LUKASI_1
Propositional Calculus
by Grzegorz Bancerek, Agata Darmochwa\l and Andrzej Trybulec
Received September 26, 1990
162. COMPLSP1
Complex Spaces
by Czes{\l}aw Byli\'nski and Andrzej Trybulec
Received September 27, 1990
163. REALSET3
Several Properties of Fields. Field Theory
by J\'ozef Bia{\l}as
Received September 27, 1990
164. SUPINF_1
Infimum and Supremum of the Set of Real Numbers. Measure Theory
by J\'ozef Bia{\l}as
Received September 27, 1990
165. SUPINF_2
Series of Positive Real Numbers. Measure Theory
by J\'ozef Bia{\l}as
Received September 27, 1990
166. ALGSTR_2
From Double Loops to Fields
by Wojciech Skaba and Micha{\l} Muzalewski
Received September 27, 1990
167. METRIC_3
Metrics in Cartesian Product
by Stanis{\l}awa Kanas and Jan Stankiewicz
Received September 27, 1990
168. SUB_METR
Submetric Spaces - Part I
by Adam Lecko and Mariusz Startek
Received September 27, 1990
Has been removed on March 23, 2010
169. METRIC_2
On Pseudometric Spaces
by Adam Lecko and Mariusz Startek
Received September 28, 1990
170. POWER
Real Exponents and Logarithms
by Konrad Raczkowski and Andrzej N\c{e}dzusiak
Received October 1, 1990
171. HESSENBE
Hessenberg Theorem
by Eugeniusz Kusak and Wojciech Leo\'nczuk
Received October 2, 1990
172. MULTOP_1
Three-Argument Operations and Four-Argument Operations
by Michal Muzalewski and Wojciech Skaba
Received October 2, 1990
173. INCPROJ
Incidence Projective Spaces
by Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
Received October 4, 1990
174. AFVECT01
One-Dimensional Congruence of Segments, Basic Facts and Midpoint Relation
by Barbara Konstanta, Urszula Kowieska, Grzegorz Lewandowski and
Krzysztof Pra\.zmowski
Received October 4, 1990
175. NORMFORM
Algebra of Normal Forms
by Andrzej Trybulec
Received October 5, 1990
176. O_RING_1
Ordered Rings - Part I
by Micha{\l} Muzalewski and Les{\l}aw W. Szczerba
Received October 11, 1990
177. O_RING_2
Ordered Rings - Part II
by Micha{\l} Muzalewski and Les{\l}aw W. Szczerba
Received October 11, 1990
Has been removed on January 22, 2007
178. O_RING_3
Ordered Rings - Part III
by Micha{\l} Muzalewski and Les{\l}aw W. Szczerba
Received October 11, 1990
Has been removed on January 22, 2007
179. MCART_2
N-Tuples and Cartesian Products for n=5
by Micha{\l} Muzalewski and Wojciech Skaba
Received October 13, 1990
Has been removed on December 9, 2011
180. MCART_3
Tuples and Cartesian Products for n=6
by Michal Muzalewski and Wojciech Skaba
Received October 15, 1990
Has been removed on March 3, 2009
181. MCART_4
Tuples and Cartesian Products for n=7
by Michal Muzalewski and Wojciech Skaba
Received October 15, 1990
Has been removed on December 18, 2007
182. MCART_5
Tuples and Cartesian Products for n=8
by Michal Muzalewski and Wojciech Skaba
Received October 15, 1990
Has been removed on March 3, 2008
183. MCART_6
Tuples and Cartesian Products for n=9
by Michal Muzalewski and Wojciech Skaba
Received October 15, 1990
Has been removed on December 8, 2007
184. ALGSTR_3
Ternary Fields
by Micha{\l} Muzalewski and Wojciech Skaba
Received October 15, 1990
185. MEASURE1
The $\sigma$-additive Measure Theory
by J\'ozef Bia{\l}as
Received October 15, 1990
186. PROJRED1
Incidence Projective Space (a reduction theorem in a plane)
by Eugeniusz Kusak and Wojciech Leo\'nczuk
Received October 16, 1990
187. MOD_1
Groups, Rings, Left- and Right-Modules
by Micha{\l} Muzalewski and Wojciech Skaba
Received October 22, 1990
Has been removed on September 23, 2008
188. LMOD_1
Finite Sums of Vectors in Left Module over Associative Ring
by Micha{\l} Muzalewski and Wojciech Skaba
Received October 22, 1990
Has been removed on January 6, 1995
189. LMOD_2
Submodules and Cosets of Submodules in Left Module over Associative Ring
by Micha{\l} Muzalewski and Wojciech Skaba
Received October 22, 1990
Has been removed on May 13, 1995
190. LMOD_3
Operations on Submodules in Left Module over Associative Ring
by Micha{\l} Muzalewski and Wojciech Skaba
Received October 22, 1990
Has been removed on May 13, 1995
191. LMOD_4
Linear Combinations in Left Module over Associative Ring
by Micha{\l} Muzalewski and Wojciech Skaba
Received October 22, 1990
Has been removed on November 19, 2003
192. LMOD_5
Linear Independence in Left Module over Domain
by Micha{\l} Muzalewski and Wojciech Skaba
Received October 22, 1990
Has been removed on January 1, 2015
193. RMOD_1
Finite Sums of Vectors in Right Module over Associative Ring
by Michal Muzalewski and Wojciech Skaba
Received October 22, 1990
Has been removed on November 19, 2003
194. RMOD_2
Submodules and Cosets of Submodules in Right Module over Associative Ring
by Michal Muzalewski and Wojciech Skaba
Received October 22, 1990
195. RMOD_3
Operations on Submodules in Right Module over Associative Ring
by Michal Muzalewski and Wojciech Skaba
Received October 22, 1990
196. RMOD_4
Linear Combinations in Right Module over Associative Ring
by Michal Muzalewski and Wojciech Skaba
Received October 22, 1990
197. RMOD_5
Linear Independence in Right Module over Domain
by Michal Muzalewski and Wojciech Skaba
Received October 22, 1990
Has been removed on June 26, 2008
198. PROCAL_1
Calculus of Propositions
by Jan Popio{\l}ek and Andrzej Trybulec
Received October 23, 1990
199. CQC_THE2
Calculus of Quantifiers. Deduction Theorem
by Agata Darmochwa\l
Received October 24, 1990
200. GEOMTRAP
A Construction of Analytical Ordered Trapezium Spaces
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
Received October 29, 1990
201. PROJRED2
On Projections in Projective Planes. Part II
by Eugeniusz Kusak, Wojciech Leo\'nczuk and Krzysztof Pra\.zmowski
Received October 31, 1990
202. CONAFFM
Metric-Affine Configurations in Metric Affine Planes - Part I
by Jolanta \'Swierzy\'nska and Bogdan \'Swierzy\'nski
Received October 31, 1990
203. CONMETR
Metric-Affine Configurations in Metric Affine Planes - Part II
by Jolanta \'Swierzy\'nska and Bogdan \'Swierzy\'nski
Received October 31, 1990
204. PAPDESAF
Fanoian, Pappian and Desarguesian Affine Spaces
by Krzysztof Pra\.zmowski
Received November 16, 1990
205. PARDEPAP
Elementary Variants of Affine Configurational Theorems
by Krzysztof Pra\.zmowski and Krzysztof Radziszewski
Received November 30, 1990
206. SEMI_AF1
Semi-Affine Space
by Eugeniusz Kusak and Krzysztof Radziszewski
Received November 30, 1990
207. AFF_4
Planes in Affine Spaces
by Wojciech Leo\'nczuk, Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
Received December 5, 1990
208. GRAPH_1
Graphs
by Krzysztof Hryniewiecki
Received December 5, 1990
209. ZF_FUND1
Mostowski's Fundamental Operations - Part I
by Andrzej Kondracki
Received December 17, 1990
210. AFPROJ
A Projective Closure and Projective Horizon of an Affine Space
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
Received December 17, 1990
211. SCHEMS_1
Schemes
by Stanis\l aw T. Czuba
Received December 17, 1990
212. HEYTING1
Algebra of Normal Forms Is a Heyting Algebra
by Andrzej Trybulec
Received January 3, 1991
213. TREES_2
K\"onig's Lemma
by Grzegorz Bancerek
Received January 10, 1991
214. FCONT_3
Monotonic and Continuous Real Function
by Jaros{\l}aw Kotowicz
Received January 10, 1991
215. FDIFF_2
Real Function Differentiability - Part II
by Jaros{\l}aw Kotowicz and Konrad Raczkowski
Received January 10, 1991
216. PRELAMB
Preliminaries to the Lambek Calculus
by Wojciech Zielonka
Received February 13, 1991
217. OPPCAT_1
Opposite Categories and Contravariant Functors
by Czes\l aw Byli\'nski
Received February 13, 1991
218. ZF_FUND2
Mostowski's Fundamental Operations - Part II
by Grzegorz Bancerek and Andrzej Kondracki
Received February 15, 1991
219. EUCLMETR
Fundamental Types of Metric Affine Spaces
by Henryk Oryszczyszyn and Krzysztof Pra\.zmowski
Received April 17, 1991
220. FILTER_1
Filters - Part II. Quotient Lattices Modulo Filters and
Direct Product of Two Lattices
by Grzegorz Bancerek
Received April 19, 1991
221. CONMETR1
Shear Theorems and Their Role in Affine Geometry
by Jolanta \'Swierzy\'nska and Bogdan \'Swierzy\'nski
Received April 19, 1991
222. SERIES_1
Series
by Konrad Raczkowski and Andrzej N\c{e}dzusiak
Received October 15, 1990
223. NAT_LAT
The Lattice of Natural Numbers and The Sublattice of it.
The Set of Prime Numbers
by Marek Chmur
Received April 26, 1991
224. GROUP_5
Commutator and Center of a Group
by Wojciech A. Trybulec
Received May 15, 1991
225. NATTRA_1
Natural Transformations. Discrete Categories
by Andrzej Trybulec
Received May 15, 1991
226. MATRIX_1
Matrices. Abelian Group of Matrices
by Katarzyna Jankowska
Received June 8, 1991
227. PCOMPS_1
Paracompact and Metrizable Spaces
by Leszek Borys
Received June 8, 1991
228. MIDSP_2
Atlas of Midpoint Algebra
by Micha{\l} Muzalewski
Received June 21, 1991
229. MEASURE2
Several Properties of the $\sigma$-additive Measure
by J\'ozef Bia{\l}as
Received July 3, 1991
230. METRIC_4
Metrics in the Cartesian Product - Part II
by Stanis\l awa Kanas and Adam Lecko
Received July 8, 1991
Has been removed on March 30, 2010
231. ALI2
Fix Point Theorem for Compact Spaces
by Alicia de la Cruz
Received July 17, 1991
232. QUIN_1
Quadratic Inequalities
by Jan Popio\l ek
Received July 19, 1991
233. BHSP_1
Introduction to Banach and Hilbert spaces - Part I
by Jan Popio{\l}ek
Received July 19, 1991
234. BHSP_2
Introduction to Banach and Hilbert spaces - Part II
by Jan Popio{\l}ek
Received July 19, 1991
235. BHSP_3
Introduction to Banach and Hilbert spaces - Part III
by Jan Popio{\l}ek
Received July 19, 1991
236. ENS_1
Category Ens
by Czes{\l}aw Byli\'nski
Received August 1, 1991
237. BORSUK_1
A Borsuk Theorem on Homotopy Types
by Andrzej Trybulec
Received August 1, 1991
238. FUNCT_6
Cartesian Product of Functions
by Grzegorz Bancerek
Received September 30, 1991
239. MODAL_1
Introduction to Modal Propositional Logic
by Alicia de la Cruz
Received September 30, 1991
240. TBSP_1
Totally Bounded Metric Spaces
by Alicia de la Cruz
Received September 30, 1991
241. GRCAT_1
Categories of Groups
by Michal Muzalewski
Received October 3, 1991
242. GROUP_6
Homomorphisms and Isomorphisms of Groups. Quotient Group
by Wojciech A. Trybulec and Micha{\l} J. Trybulec
Received October 3, 1991
243. MOD_2
Rings and Modules - Part II
by Michal Muzalewski
Received October 18, 1991
244. MOD_3
Free Modules
by Michal Muzalewski
Received October 18, 1991
245. ANALORT
Oriented Metric-Affine Plane - Part I
by Jaroslaw Zajkowski
Received October 24, 1991
246. EUCLID
The Euclidean Space
by Agata Darmochwa{\l}
Received November 21, 1991
247. TOPMETR
Metric Spaces as Topological Spaces - Fundamental Concepts
by Agata Darmochwa{\l} and Yatsuka Nakamura
Received November 21, 1991
248. HEINE
Heine--Borel's Covering Theorem
by Agata Darmochwa{\l} and Yatsuka Nakamura
Received November 21, 1991
249. TOPMETR2
Some Facts about Union of Two Functions and Continuity of Union of Functions
by Yatsuka Nakamura and Agata Darmochwa{\l}
Received November 21, 1991
250. TOPREAL1
The Topological Space ${\calE}^2_{\rm T}$.
Arcs, Line Segments and Special Polygonal Arcs
by Agata Darmochwa{\l} and Yatsuka Nakamura
Received November 21, 1991
251. GR_CY_1
Cyclic Groups and Some of Their Properties - Part I
by Dariusz Surowik
Received November 22, 1991
252. ISOCAT_1
Isomorphisms of Categories
by Andrzej Trybulec
Received November 22, 1991
253. CQC_SIM1
Similarity of Formulae
by Agata Darmochwa{\l} and Andrzej Trybulec
Received November 22, 1991
254. RINGCAT1
Category of Rings
by Micha{\l} Muzalewski
Received December 5, 1991
255. MODCAT_1
Category of Left Modules
by Micha{\l} Muzalewski
Received December 12, 1991
256. FDIFF_3
Real Function One-Side Differantiability
by Ewa Burakowska and Beata Madras
Received December 12, 1991
257. METRIC_6
Sequences in Metric Spaces
by Stanis{\l}awa Kanas and Adam Lecko
Received December 12, 1991
258. TOPREAL2
The Topological Space ${\calE}^2_{\rm T}$. Simple Closed Curves
by Agata Darmochwa{\l} and Yatsuka Nakamura
Received December 30, 1991
259. TSEP_1
Separated and Weakly Separated Subspaces of Topological Spaces
by Zbigniew Karno
Received January 8, 1992
260. SYSREL
Some Properties of Binary Relations
by Waldemar Korczy\'nski
Received January 17, 1992
261. FF_SIEC
Definitions of Petri Net - Part I
by Waldemar Korczy\'nski
Received January 31, 1992
262. E_SIEC
Definitions of Petri Net - Part II
by Waldemar Korczy\'nski
Received January 31, 1992
263. S_SIEC
Definitions of Petri Net - Part III
by Waldemar Korczy\'nski
Received January 31, 1992
Has been removed on November 19, 2003
264. L_HOSPIT
The de l'Hospital Theorem
by Ma{\l}gorzata Korolkiewicz
Received February 20, 1992
265. COMMACAT
Comma Category
by Grzegorz Bancerek and Agata Darmochwa\l
Received February 20, 1992
266. LANG1
Context-Free Grammar - Part 1
by Patricia L. Carlson and Grzegorz Bancerek
Received February 21, 1992
267. MEASURE3
Completeness of the $\sigma$-Additive Measure. Measure Theory
by J\'ozef Bia{\l}as
Received February 22, 1992
268. BHSP_4
Series in Banach and Hilbert Spaces
by El\.zbieta Kraszewska and Jan Popio{\l}ek
Received April 1, 1992
269. CAT_3
Products and Coproducts in Categories
by Czes{\l}aw Byli\'nski
Received May 11, 1992
270. MATRIX_2
Transpose Matrices and Groups of Permutations
by Katarzyna Jankowska
Received May 20, 1992
Has been removed on November 10, 2013
271. LATTICE3
Complete Lattices
by Grzegorz Bancerek
Received May 13, 1992
272. TMAP_1
Continuity of Mappings over the Union of Subspaces
by Zbigniew Karno
Received May 22, 1992
273. SEQFUNC
Functional Sequence from a Domain to a Domain
by Beata Perkowska
Received May 22, 1992
274. MIDSP_3
Reper Algebras
by Micha{\l} Muzalewski
Received May 28, 1992
275. GR_CY_2
Isomorphisms of Cyclic Groups. Some Properties of Cyclic Groups
by Dariusz Surowik
Received June 5, 1992
276. ISOCAT_2
Some Isomorphisms Between Functor Categories
by Andrzej Trybulec
Received June 5, 1992
277. TDLAT_1
The Lattice of Domains of a Topological Space
by Toshihiko Watanabe
Received June 12, 1992
278. LMOD_6
Submodules
by Micha{\l} Muzalewski
Received June 19, 1992
279. DIRORT
Oriented Metric-Affine Plane - Part II
by Jaros{\l}aw Zajkowski
Received June 19, 1992
280. MOD_4
Opposite Rings, Modules and their Morphisms
by Micha{\l} Muzalewski
Received June 22, 1992
281. MEASURE4
Properties of Caratheodor's Measure
by J\'ozef Bia{\l}as
Received June 25, 1992
282. TDLAT_2
Completeness of the Lattices of Domains of a Topological Space
by Zbigniew Karno and Toshihiko Watanabe
Received July 16, 1992
283. PCOMPS_2
On Paracompactness of Metrizable Spaces
by Leszek Borys
Received July 23, 1992
284. TREAL_1
The Brouwer Fixed Point Theorem for Intervals
by Toshihiko Watanabe
Received August 17, 1992
285. CARD_5
On Powers of Cardinals
by Grzegorz Bancerek
Received August 24, 1992
286. TOPREAL3
Basic Properties of Connecting Points with Line Segments in ${\calE}^2_{\rm T}$
by Yatsuka Nakamura and Jaros{\l}aw Kotowicz
Received August 24, 1992
287. TOPREAL4
Connectedness Conditions Using Polygonal Arcs
by Yatsuka Nakamura and Jaros{\l}aw Kotowicz
Received August 24, 1992
288. GOBOARD1
Introduction to Go-Board - Part I. Basic Notations
by Jaros{\l}aw Kotowicz and Yatsuka Nakamura
Received August 24, 1992
289. GOBOARD2
Introduction to Go-Board - Part II.
Go-Board Determined by Finite Sequence of point from ${\calE}^2_{\rm T}$
by Jaros{\l}aw Kotowicz and Yatsuka Nakamura
Received August 24, 1992
290. GOBOARD3
Properties of Go-Board - Part III
by Jaros{\l}aw Kotowicz and Yatsuka Nakamura
Received August 24, 1992
291. GOBOARD4
Go-Board Theorem
by Jaros{\l}aw Kotowicz and Yatsuka Nakamura
Received August 24, 1992
292. JORDAN1
The Jordan's Property for Certain Subsets of the Plane
by Yatsuka Nakamura and Jaros{\l}aw Kotowicz
Received August 24, 1992
293. TDLAT_3
The Lattice of Domains of an Extremally Disconnected Space
by Zbigniew Karno
Received August 27, 1992
294. AMI_1
A Mathematical Model of CPU
by Yatsuka Nakamura and Andrzej Trybulec
Received October 14, 1992
Has been removed on April 7, 2011 (partially covered by EXTPRO_1)
295. CAT_4
Cartesian Categories
by Czes{\l}aw Byli\'nski
Received October 27, 1992
296. VFUNCT_1
Algebra of Vector Functions
by Hiroshi Yamazaki and Yasunari Shidama
Received October 27, 1992
297. TSEP_2
On a Duality Between Weakly Separated Subspaces of Topological Spaces
by Zbigniew Karno
Received November 9, 1992
298. PETRI
Basic Petri Net Concepts.
Place/Transition Net Structure, Deadlocks, Traps, Dual Nets
by Pauline N. Kawamoto, Yasushi Fuwa and Yatsuka Nakamura
Received November 27, 1992
299. FIN_TOPO
Finite Topological Spaces. Finite Topology Concepts and Neighbourhoods
by Hiroshi Imura and Masayoshi Eguchi
Received November 27, 1992
300. TREES_3
Sets and Functions of Trees and Joining Operations of Trees
by Grzegorz Bancerek
Received November 27, 1992
301. FVSUM_1
Sum and Product of Finite Sequences of Elements of a Field
by Katarzyna Zawadzka
Received December 29, 1992
302. AMI_2
On a Mathematical Model of Programs
by Yatsuka Nakamura and Andrzej Trybulec
Received December 29, 1992
303. UNIALG_1
Basic Notation of Universal Algebra
by Jaros{\l}aw Kotowicz, Beata Madras and Ma{\l}gorzata Korolkiewicz
Received December 29, 1992
304. COH_SP
Coherent Space
by Jaros{\l}aw Kotowicz and Konrad Raczkowski
Received December 29, 1992
305. MONOID_0
Monoids
by Grzegorz Bancerek
Received December 29, 1992
306. MONOID_1
Monoid of Multisets and Subsets
by Grzegorz Bancerek
Received December 29, 1992
307. PRVECT_1
Product of Families of Groups and Vector Spaces
by Anna Lango and Grzegorz Bancerek
Received December 29, 1992
308. MEASURE5
Properties of the Intervals of Real Numbers
by J\'ozef Bia{\l}as
Received January 12, 1993
309. RLVECT_4
Subspaces of Real Linear Space Generated by One, Two, or Three Vectors
and Their Cosets
by Wojciech A. Trybulec
Received February 24, 1993
310. LMOD_7
Domains of Submodules, Join and Meet of Finite Sequences of Submodules
and Quotient Modules
by Micha{\l} Muzalewski
Received March 29, 1993
311. RFINSEQ
Functions and Finite Sequences of Real Numbers
by Jaros{\l}aw Kotowicz
Received March 15, 1993
312. RFUNCT_3
Properties of Partial Functions from a Domain to the Set of Real Numbers
by Jaros{\l}aw Kotowicz and Yuji Sakai
Received March 15, 1993
313. TOPS_3
Remarks on Special Subsets of Topological Spaces
by Zbigniew Karno
Received April 6, 1993
314. TEX_1
On Discrete and Almost Discrete Topological Spaces
by Zbigniew Karno
Received April 6, 1993
315. MATRIX_3
The Product of Matrices of Elements of a Field and Determinants
by Katarzyna Zawadzka
Received May 17, 1993
316. REARRAN1
Introduction to Theory of Rearrangment
by Yuji Sakai and Jaros{\l}aw Kotowicz
Received May 22, 1993
317. PBOOLE
Manysorted Sets
by Andrzej Trybulec
Received July 7, 1993
318. UNIALG_2
Subalgebras of the Universal Algebra. Lattices of Subalgebras
by Ewa Burakowska
Received July 8, 1993
319. HAHNBAN
Hahn Banach Theorem
by Bogdan Nowak and Andrzej Trybulec
Received July 8, 1993
320. LATTICE4
Homomorphisms of Lattices \\ Finite Join and Finite Meet
by Jolanta Kamie\'nska and Jaros\l aw Stanis\l aw Walijewski
Received July 14, 1993
321. OPENLATT
Representation Theorem for Heyting Lattices
by Jolanta Kamie\'nska
Received July 14, 1993
322. LOPCLSET
Representation Theorem for Boolean Algebras
by Jaros{\l}aw Stanis{\l}aw Walijewski
Received July 14, 1993
323. AMI_3
Some Remarks on Simple Concrete Model of Computer
by Andrzej Trybulec and Yatsuka Nakamura
Received October 8, 1993
324. AMI_4
Euclide Algorithm
by Andrzej Trybulec and Yatsuka Nakamura
Received October 8, 1993
325. SCM_1
Development of Terminology for {\bf SCM}
by Grzegorz Bancerek and Piotr Rudnicki
Received October 8, 1993
326. PRE_FF
Two Programs for {\bf SCM}. Part I - Preliminaries
by Grzegorz Bancerek and Piotr Rudnicki
Received October 8, 1993
327. FIB_FUSC
Two Programs for {\bf SCM}. Part II - Proofs
by Grzegorz Bancerek and Piotr Rudnicki
Received October 8, 1993
328. TREES_4
Joining of Decorated Trees
by Grzegorz Bancerek
Received October 8, 1993
329. BINARITH
Binary Arithmetics. Addition
by Takaya Nishiyama and Yasuho Mizuhara
Received October 8, 1993
330. BOOLMARK
Basic Concepts for Petri Nets with Boolean Markings.
Boolean Markings and the Firability/Firing of Transitions
by Pauline N. Kawamoto, Yasushi Fuwa and Yatsuka Nakamura
Received October 8, 1993
331. DTCONSTR
On Defining Functions on Trees
by Grzegorz Bancerek and Piotr Rudnicki
Received October 12, 1993
332. PRALG_1
Product of Family of Universal Algebras
by Beata Madras
Received October 12, 1993
333. ALG_1
Homomorphisms of algebras. Quotient Universal Algebra
by Ma{\l}gorzata Korolkiewicz
Received October 12, 1993
334. FREEALG
Free Universal Algebra Construction
by Beata Perkowska
Received October 20, 1993
335. COMSEQ_1
Complex Sequences
by Agnieszka Banachowicz and Anna Winnicka
Received November 5, 1993
336. TEX_2
Maximal Discrete Subspaces of Almost Discrete Topological Spaces
by Zbigniew Karno
Received November 5, 1993
337. TEX_3
On Nowhere and Everywhere Dense Subspaces of Topological Spaces
by Zbigniew Karno
Received November 9, 1993
338. AMI_5
On the Decomposition of the States of SCM
by Yasushi Tanaka
Received November 23, 1993
339. BINTREE1
On Defining Functions on Binary Trees
by Grzegorz Bancerek and Piotr Rudnicki
Received December 30, 1993
340. SCM_COMP
A compiler of arithmetic expressions for { \bf SCM }
by Grzegorz Bancerek and Piotr Rudnicki
Received December 30, 1993
341. MEASURE6
Some Properties of the Intervals
by J\'{o}zef Bia\l{}as
Received February 5, 1994
342. BINARI_2
Binary Arithmetics.Addition and Subtraction of Integers
by Yasuho Mizuhara and Takaya Nishiyama
Received March 18, 1994
343. BOOLEALG
Boolean Properties of Lattices
by Agnieszka Julia Marasik
Received March 28, 1994
344. MSUALG_1
Many Sorted Algebras
by Andrzej Trybulec
Received April 21, 1994
345. AUTGROUP
On the Group of Inner Automorphisms
by Artur Korni{\l}owicz
Received April 22, 1994
346. MSUALG_2
Subalgebras of a Many Sorted Algebra. Lattice of Subalgerbas
by Ewa Burakowska
Received April 25, 1994
347. PRALG_2
Products of Many Sorted Algebras
by Beata Madras
Received April 25, 1994
348. MSUALG_3
Homomorphisms of Many Sorted Algebras
by Ma{\l}gorzata Korolkiewicz
Received April 25, 1994
349. MSAFREE
Free Many Sorted Universal Algebra. Lattice of Subalgerbas
by Beata Perkowska
Received April 27, 1994
350. T_0TOPSP
$T_0$ Topological Spaces
by Mariusz \.Zynel and Adam Guzowski
Received May 6, 1994
351. MSUALG_4
Many Sorted Quotient Algebra
by Ma{\l}gorzata Korolkiewicz
Received May 6, 1994
352. QUANTAL1
Quantales
by Grzegorz Bancerek
Received May 9, 1994
353. TOPRNS_1
Sequences in $R^n$
by Agnieszka Sakowicz , Jaros{\l}aw Gryko and Adam Grabowski
Received May 10, 1994
354. SPPOL_1
Extremal Properties of Vertices on Special Polygons I
by Yatsuka Nakamura and Czes\law Byli\'nski
Received May 11, 1994
355. RELOC
Relocatability
by Yasushi Tanaka
Received June 16, 1994
356. TEX_4
Maximal Anti-Discrete Subspaces of Topological Spaces
by Zbigniew Karno
Received July 26, 1994
357. TSP_1
On Kolmogorov Topological Spaces
by Zbigniew Karno
Received July 26, 1994
358. TSP_2
Maximal Kolmogorov Subspaces of a Topological Space as Stone
Retracts of the Ambient Space
by Zbigniew Karno
Received July 26, 1994
359. PROJPL_1
Projective { P } lanes
by Micha{\l} Muzalewski
Received July 28, 1994
360. SGRAPH1
the formalisation of simple graphs
by Yozo Toda
Received September 8, 1994
361. GRSOLV_1
Solvable Groups
by Katarzyna Zawadzka
Received October 23, 1994
362. FILTER_2
Ideals
by Grzegorz Bancerek
Received October 24, 1994
363. CAT_5
Categorial Categories and Slice Categories
by Grzegorz Bancerek
Received October 24, 1994
364. PRE_CIRC
Preliminaries to Circuits, I
by Yatsuka Nakamura , Piotr Rudnicki , Andrzej Trybulec
and Pauline N. Kawamoto
Received November 17, 1994
365. FSM_1
Minimization of finite state machines
by Miroslava Kaloper and Piotr Rudnicki
Received November 18, 1994
366. TREES_9
Subtrees
by Grzegorz Bancerek
Received November 25, 1994
367. MSATERM
Terms over many sorted universal algebra
by Grzegorz Bancerek
Received November 25, 1994
368. DECOMP_1
On the Decomposition of the Continuity
by Marian Przemski
Received December 12, 1994
369. MSAFREE1
A Scheme for Extensions of Homomorphisms of Manysorted
Algebras
by Andrzej Trybulec
Received December 13, 1994
370. MSUHOM_1
The Correspondence Between Homomorphisms of Universal Algebra
& Manysorted Algebra
by Adam Grabowski
Received December 13, 1994
371. MSAFREE2
Preliminaries to Circuits, II
by Yatsuka Nakamura , Piotr Rudnicki , Andrzej Trybulec and Pauline N. Kawamoto
Received December 13, 1994
372. AUTALG_1
On the Group of Automorphisms of Universal Algebra & Many
Sorted Algebra
by Artur Korni{\l}owicz
Received December 13, 1994
373. CIRCUIT1
Introduction to Circuits, I
by Yatsuka Nakamura , Piotr Rudnicki , Andrzej Trybulec and Pauline N. Kawamoto
Received December 15, 1994
374. CANTOR_1
The Cantor Set
by Alexander Yu. Shibakov and Andrzej Trybulec
Received January 9, 1995
375. CQC_THE3
Logical Equivalence of Formulae
by Oleg Okhotnikov
Received January 24, 1995
376. FINSEQ_5
Some Properties of Restrictions of Finite Sequences
by Czes\law Byli\'nski
Received January 25, 1995
377. SPPOL_2
Special Polygons
by Czes\law Byli\'nski and Yatsuka Nakamura
Received January 30, 1995
378. MEASURE7
The One-Dimensional Lebesgue Measure As an Example of a
Formalization in the Mizar Language of the Classical
Definition of a Mathematical Object
by J\'ozef Bia{\l}as
Received February 4, 1995
379. ALTCAT_1
Categories without Uniqueness of { \bf cod } and { \bf dom }
by Andrzej Trybulec
Received February 28, 1995
380. EXTENS_1
Extensions of Mappings on Generator Set
by Artur Korni{\l}owicz
Received March 23, 1995
381. CIRCUIT2
Introduction to Circuits, II
by Yatsuka Nakamura , Piotr Rudnicki , Andrzej Trybulec and Pauline N. Kawamoto
Received April 10, 1995
382. MBOOLEAN
Definitions and Basic Properties of Boolean & Union of Many
Sorted Sets
by Artur Korni{\l}owicz
Received April 27, 1995
383. CIRCCOMB
Combining of Circuits
by Yatsuka Nakamura and Grzegorz Bancerek
Received May 11, 1995
384. GRAPH_2
Vertex sequences induced by chains
by Yatsuka Nakamura and Piotr Rudnicki
Received May 13, 1995
385. VECTSP_8
On the Lattice of Subspaces of Vector Space
by Andrzej Iwaniuk
Received May 23, 1995
386. LATSUBGR
On the Lattice of Subgroups of a Group
by Janusz Ganczarski
Received May 23, 1995
387. UNIALG_3
On the Lattice of Subalgebras of a Universal Algebra
by Miros{\l}aw Jan Paszek
Received May 23, 1995
388. FINSEQ_6
On the Decomposition of Finite Sequences
by Andrzej Trybulec
Received May 24, 1995
389. GOBOARD5
Decomposing a Go Board into Cells
by Yatsuka Nakamura and Andrzej Trybulec
Received May 26, 1995
390. INDEX_1
Indexed Category
by Grzegorz Bancerek
Received June 8, 1995
391. MATRLIN
Associated Matrix of Linear Map
by Robert Milewski
Received June 30, 1995
392. GOBOARD6
On the Geometry of a Go-board
by Andrzej Trybulec
Received July 9, 1995
393. WEIERSTR
The Theorem of Weierstrass
by J\'ozef Bia\las and Yatsuka Nakamura
Received July 10, 1995
394. URYSOHN1
Dyadic Numbers and $T_4$ Topological Spaces
by J\'ozef Bia\las and Yatsuka Nakamura
Received July 29, 1995
395. FACIRC_1
Full Adder Circuit. Part { I }
by Grzegorz Bancerek and Yatsuka Nakamura
Received August 10, 1995
396. COHSP_1
Continuous, Stable, and Linear Maps of Coherence Spaces
by Grzegorz Bancerek
Received August 30, 1995
397. PZFMISC1
Some Basic Properties of Many Sorted Sets
by Artur Korni{\l}owicz
Received September 29, 1995
398. TREES_A
Replacement of Subtrees in a Tree
by Oleg Okhotnikov
Received October 1, 1995
399. PUA2MSS1
Minimal Manysorted Signature for Partial Algebra
by Grzegorz Bancerek
Received October 1, 1995
400. QC_LANG4
The Subformula Tree of a Formula of the First Order
Language
by Oleg Okhotnikov
Received October 2, 1995
401. VECTSP_9
Steinitz Theorem and Dimension of a Vector Space
by Mariusz \.Zynel
Received October 6, 1995
402. GOBOARD7
On the Go Board of a Standard Special Circular Sequence
by Andrzej Trybulec
Received October 15, 1995
403. ENDALG
On the Monoid of Endomorphisms of Universal Algebra \& Many
Sorted Algebra
by Jaros{\l}aw Gryko
Received October 17, 1995
404. GOBOARD8
More on Segments on a Go Board
by Andrzej Trybulec
Received October 17, 1995
405. MSSUBFAM
Certain Facts about Families of Subsets of Many Sorted Sets
by Artur Korni{\l}owicz
Received October 27, 1995
406. TRIANG_1
On the concept of the triangulation
by Beata Madras
Received October 28, 1995
407. GOBOARD9
Left and Right Component of the Complement of a Special
Closed Curve
by Andrzej Trybulec
Received October 29, 1995
408. REWRITE1
Reduction Relations
by Grzegorz Bancerek
Received November 14, 1995
409. MSUALG_5
Lattice of Congruences in a Many Sorted Algebra
by Robert Milewski
Received January 11, 1996
410. FUNCT_7
Miscellaneous Facts about Functions
by Grzegorz Bancerek and Andrzej Trybulec
Received January 12, 1996
411. ALTCAT_2
Examples of Category Structures.Subcategories
by Andrzej Trybulec
Received January 22, 1996
412. ORDERS_3
On the Category of Posets
by Adam Grabowski
Received January 22, 1996
413. SCMFSA_1
An Extension of { \bf SCM }
by Andrzej Trybulec , Yatsuka Nakamura and Piotr Rudnicki
Received February 3, 1996
414. CONNSP_3
Components and Unions of Components
by Yatsuka Nakamura and Andrzej Trybulec
Received February 5, 1996
415. SCMFSA_2
The { \bf SCM_FSA } computer
by Andrzej Trybulec , Yatsuka Nakamura and Piotr Rudnicki
Received February 7, 1996
416. CLOSURE1
On the Many Sorted Closure Operator and the Many Sorted
Closure System
by Artur Korni{\l}owicz
Received February 7, 1996
417. SCMFSA_3
Computation in { \bf SCM_FSA }
by Andrzej Trybulec and Yatsuka Nakamura
Received February 7, 1996
418. CLOSURE2
On the Closure Operator and the Closure System of Many
Sorted Sets
by Artur Korni{\l}owicz
Received February 7, 1996
419. MSUALG_6
Translations and Endomorphisms in Many Sorted Algebras.Stable
Equational Theories
by Grzegorz Bancerek
Received February 9, 1996
420. MSUALG_7
More on the Lattice of Many Sorted Equivalence Relations
by Robert Milewski
Received February 9, 1996
421. SCMFSA_4
Modifying addresses of instructions of { \bf SCM_FSA }
by Andrzej Trybulec and Yatsuka Nakamura
Received February 14, 1996
422. MSSCYC_1
The correspondence between monotonic many sorted signatures
and well-founded graphs
by Czes{\l}aw Byli\'nski and Piotr Rudnicki
Received February 14, 1996
423. SCMFSA_5
Relocability for { \bf SCM_FSA }
by Andrzej Trybulec and Yatsuka Nakamura
Received February 22, 1996
424. MSUALG_8
More on the Lattice of Congruences in a Many Sorted Algebra
by Robert Milewski
Received March 6, 1996
425. MSSCYC_2
The correspondence between monotonic many sorted signatures
and well founded graphs. Part II
by Czes{\l}aw Byli\'nski and Piotr Rudnicki
Received April 10, 1996
426. FUNCTOR0
Functors for Alternative Categories
by Andrzej Trybulec
Received April 24, 1996
427. FUNCTOR1
Basic Properties about Functor Structures
by Claus Zinn and Wolfgang Jaksch
Received April 24, 1996
428. SCMFSA_7
Some Multi-instructions defined by sequence of instructions
of SCM+FSA
by Noriko Asamoto
Received April 24, 1996
429. PRALG_3
More on Products of Many Sorted Algebras
by Mariusz Giero
Received April 29, 1996
430. GOBRD10
Adjacency Concept for Pairs of Natural Numbers
by Yatsuka Nakamura and Andrzej Trybulec
Received June 10, 1996
431. MSALIMIT
Inverse Limits of Many Sorted Algebras
by Adam Grabowski
Received June 11, 1996
432. MSUALG_9
On the Trivial Many Sorted Algebras and Many Sorted
Congruences
by Artur Korni\l owicz
Received June 11, 1996
433. MSINST_1
Examples of Category Structures
by Adam Grabowski
Received June 11, 1996
434. SCMFSA6A
On the compositions of macro instructions
by Andrzej Trybulec , Yatsuka Nakamura and Noriko Asamoto
Received June 20, 1996
435. SF_MASTR
Memory handling for SCM+FSA
by Piotr Rudnicki and Andrzej Trybulec
Received July 18, 1996
436. GOBRD11
Some Topological Properties of Cells in Rư
by Yatsuka Nakamura and Andrzej Trybulec
Received July 22, 1996
437. SCMFSA6B
On the compositions of macro instructions, Part II
by Noriko Asamoto , Yatsuka Nakamura , Piotr Rudnicki and Andrzej Trybulec
Received July 22, 1996
438. GOBRD12
The First Part of Jordan's Theorem for Special Polygons
by Yatsuka Nakamura and Andrzej Trybulec
Received July 22, 1996
439. SCMFSA6C
On the compositions of macro instructions, Part III
by Noriko Asamoto , Yatsuka Nakamura , Piotr Rudnicki and Andrzej Trybulec
Received July 22, 1996
440. SCMFSA7B
Constant assignment macro instructions of SCM+FSA, Part II
by Noriko Asamoto
Received August 27, 1996
441. SCMFSA8A
Conditional branch macro instructions of SCM+FSA, Part
I(preliminary)
by Noriko Asamoto
Received August 27, 1996
442. SCMFSA8B
Conditional branch macro instructions of SCM+FSA, Part II
by Noriko Asamoto
Received August 27, 1996
443. YELLOW_0
Bounds in Posets and Relational Substructures
by Grzegorz Bancerek
Received September 10, 1996
444. WAYBEL_0
Directed Sets, Nets, Ideals, Filters, and Maps
by Grzegorz Bancerek
Received September 12, 1996
445. KNASTER
Fix-points in complete lattices
by Piotr Rudnicki and Andrzej Trybulec
Received September 16, 1996
446. YELLOW_1
Boolean Posets, Posets under Inclusion and Products of
Relational Structures
by Adam Grabowski and Robert Milewski
Received September 20, 1996
447. YELLOW_2
Properties of Relational Structures, Posets, Lattices and Maps
by Mariusz \.Zynel and Czes{\l}aw Byli\'nski
Received September 20, 1996
448. WAYBEL_1
Galois Connections
by Czes\law Byli\'nski
Received September 25, 1996
449. YELLOW_3
Cartesian Products of Relations and Relational Structures
by Artur Korni{\l}owicz
Received September 25, 1996
450. YELLOW_4
Definitions and Properties of the Join and Meet of Subsets
by Artur Korni{\l}owicz
Received September 25, 1996
451. WAYBEL_2
Meet - continuous Lattices
by Artur Korni{\l}owicz
Received October 10, 1996
452. WAYBEL_3
The "Way-Below" Relation
by Grzegorz Bancerek
Received October 11, 1996
453. WAYBEL_4
Auxiliary and Approximating Relations
by Adam Grabowski
Received October 21, 1996
454. TWOSCOMP
2's Complement Circuit. Part I.Boolean Operators and 2's
Complement Circuit Properties
by Katsumi Wasaki and Pauline N. Kawamoto
Received October 25, 1996
455. WAYBEL_5
The Equational Characterization
by Mariusz \.Zynel
Received October 25, 1996
456. YELLOW_5
Miscellaneous Facts about Relation Structure
by Agnieszka Julia Marasik
Received November 8, 1996
457. YELLOW_6
Moore-Smith Convergence
by Andrzej Trybulec
Received November 12, 1996
458. YELLOW_7
Duality in Relation Structures
by Grzegorz Bancerek
Received November 12, 1996
459. WAYBEL_6
Irreducible and Prime Elements
by Beata Madras
Received December 1, 1996
460. WAYBEL_7
Prime Ideals and Filters
by Grzegorz Bancerek
Received December 1, 1996
461. WAYBEL_8
Algebraic Lattices
by Robert Milewski
Received December 1, 1996
462. JORDAN3
Reconstructions of Special Sequences
by Yatsuka Nakamura and Roman Matuszewski
Received December 10, 1996
463. COMSEQ_2
Conjugate Sequences, Bounded Complex Sequences and Convergent
Complex Sequences
by Adam Naumowicz
Received December 20, 1996
464. WAYBEL_9
On The Topological Properties of Meet-Continuous Lattices
by Artur Korni{\l}owicz
Received December 20, 1996
465. INSTALG1
Institution of Many-sorted Algebras, Part { I } : Signature
Reduct of an Algebra
by Grzegorz Bancerek
Received December 30, 1996
466. YELLOW_8
Baire Spaces, Sober Spaces
by Andrzej Trybulec
Received January 8, 1997
467. WAYBEL10
Closure Operators and Subalgebras
by Grzegorz Bancerek
Received January 15, 1997
468. CATALG_1
Algebra of Morphisms
by Grzegorz Bancerek
Received January 28, 1997
469. WAYBEL11
Scott Topology
by Andrzej Trybulec
Received January 29, 1997
470. WAYBEL12
On the Baire Category Theorem
by Artur Korni{\l}owicz
Received February 5, 1997
471. ALTCAT_3
Basic properties of objects and morphisms.In categories
without Uniqueness of { \bf cod } and { \bf dom }
by Beata Madras
Received February 14, 1997
472. ABIAN
Abian's Fixed Point Theorem
by Piotr Rudnicki and Andrzej Trybulec
Received February 22, 1997
473. WELLFND1
On same equivalents of well-foundedness
by Piotr Rudnicki and Andrzej Trybulec
Received February 25, 1997
474. WAYBEL13
Algebraic and Arithmetic Lattices
by Robert Milewski
Received March 4, 1997
475. JORDAN4
Subsequences of Standard Special Circular Sequences in
${\cal E}^2_{\rm T}$
by Yatsuka Nakamura , Roman Matuszewski and Adam Grabowski
Received May 12, 1997
476. SUBSTLAT
Lattice of Substitutions
by Adam Grabowski
Received May 21, 1997
477. EQUATION
Equations in Many Sorted Algebras
by Artur Korni{\l}owicz
Received May 30, 1997
478. FUNCTOR2
Category of Functors between Alternative Categories
by Robert Nieszczerzewski
Received June 12, 1997
479. YONEDA_1
Yoneda Embedding
by Miros{\l}aw Wojciechowski
Received June 12, 1997
480. GCD_1
The correctness of the Generic Algorithms of Brown and Henrici
concerning Addition and Multiplication in Fraction Fields
by Christoph Schwarzweller
Received June 16, 1997
481. BIRKHOFF
Birkhoff Theorem for Many Sorted Algebras
by Artur Korni{\l}owicz
Received June 19, 1997
482. CLOSURE3
Algebraic Operation on Subsets of Many Sorted Sets
by Agnieszka Julia Marasik
Received June 23, 1997
483. COMSEQ_3
Convergence and the Limit of Complex Sequences. Series
by Yasunari Shidama and Artur Korni{\l}owicz
Received June 25, 1997
484. RLVECT_5
The Steinitz Theorem and the Dimension of a Real Linear
Space
by JingChao Chen
Received July 1, 1997
485. GRAPH_3
Euler circuits and paths
by Yatsuka Nakamura and Piotr Rudnicki
Received July 29, 1997
486. PSCOMP_1
Bounding boxes for compact sets in ${\calE}^2$
by Czes{\l}aw Byli\'nski and Piotr Rudnicki
Received July 29, 1997
487. WAYBEL14
The Scott topology, Part II
by Czes{\l}aw Byli\'nski and Piotr Rudnicki
Received August 27, 1997
488. BORSUK_2
Introduction to Homotopy Theory
by Adam Grabowski
Received September 10, 1997
489. JORDAN5A
Some Properties of Real Maps
by Adam Grabowski and Yatsuka Nakamura
Received September 10, 1997
490. JORDAN5B
The Ordering of Points on a Curve, Part { I }
by Adam Grabowski and Yatsuka Nakamura
Received September 10, 1997
491. JORDAN5C
The Ordering of Points on a Curve, Part { II }
by Adam Grabowski and Yatsuka Nakamura
Received September 10, 1997
492. ALTCAT_4
On the Categories Without Uniqueness of { \bf cod } and {
\bf dom } . Some Properties of the Morphisms and the
Functors
by Artur Korni{\l}owicz
Received October 3, 1997
493. SCMFSA8C
The { \bf loop } and { \bf Times } Macroinstruction for {
\SCMFSA }
by Noriko Asamoto
Received October 29, 1997
494. WAYBEL15
More on the Algebraic and Arithmetic Lattices
by Robert Milewski
Received October 29, 1997
495. JORDAN2B
Projections in n-Dimensional Euclidean Space to Each
Coordinates
by Roman Matuszewski and Yatsuka Nakamura
Received November 3, 1997
496. TOPREAL5
Intermediate Value Theorem and Thickness of Simple Closed
Curves
by Yatsuka Nakamura and Andrzej Trybulec
Received November 13, 1997
497. LATTICE5
J\'onson Theorem
by Jaros{\l}aw Gryko
Received November 13, 1997
498. UNIFORM1
Lebesgue's Covering Lemma, Uniform Continuity and Segmentation
of Arcs
by Yatsuka Nakamura and Andrzej Trybulec
Received November 13, 1997
499. SPRECT_1
On Rectangular Finite Sequences of the Points of the Plane
by Andrzej Trybulec and Yatsuka Nakamura
Received November 30, 1997
500. SPRECT_2
On the Order on a Special Polygon
by Andrzej Trybulec and Yatsuka Nakamura
Received November 30, 1997
501. EULER_1
Euler's Function
by Yoshinori Fujisawa and Yasushi Fuwa
Received December 10, 1997
502. SCMFSA_9
While Macro Instructions of SCM+FSA
by Jing-Chao Chen
Received December 10, 1997
503. JORDAN6
A Decomposition of Simple Closed Curves and an Order of
Their Points
by Yatsuka Nakamura and Andrzej Trybulec
Received December 19, 1997
504. WSIERP_1
The Chinese Remainder Theorem
by Andrzej Kondracki
Received December 30, 1997
505. FUNCTOR3
The Composition of Functors and Transformations in
Alternative Categories
by Artur Korni{\l}owicz
Received January 21, 1998
506. WAYBEL16
Completely-Irreducible Elements
by Robert Milewski
Received February 9, 1998
507. WAYBEL17
Scott-Continuous Functions
by Adam Grabowski
Received February 13, 1998
508. NAT_2
Natural Numbers
by Robert Milewski
Received February 23, 1998
509. BINARI_3
Binary Arithmetics. Binary Sequences
by Robert Milewski
Received February 24, 1998
510. BINTREE2
Full Trees
by Robert Milewski
Received February 25, 1998
511. T_1TOPSP
On $T_{1}$ Reflex of Topological Space
by Adam Naumowicz and Mariusz {\L}api\'nski
Received March 7, 1998
512. YELLOW_9
Bases and Refinements of Topologies
by Grzegorz Bancerek
Received March 9, 1998
513. YELLOW10
The Properties of Product of Relational Structures
by Artur Korni{\l}owicz
Received March 27, 1998
514. YELLOW11
On the Characterization of Modular and Distributive Lattices
by Adam Naumowicz
Received April 3, 1998
515. WAYBEL18
Injective Spaces
by Jaros{\l}aw Gryko
Received April 17, 1998
516. YELLOW12
On the Characterization of Hausdorff Spaces
by Artur Korni{\l}owicz
Received April 18, 1998
517. QUOFIELD
The Field of Quotients over an Integral Domain
by Christoph Schwarzweller
Received May 4, 1998
518. FRECHET
First-countable, Sequential, and Frechet Spaces
by Bart{\l}omiej Skorulski
Received May 13, 1998
519. SFMASTR1
On the Composition of non-parahalting Macro Instructions
by Piotr Rudnicki
Received June 3, 1998
520. SCMFSA9A
The { \bf while } macro instructions of SCM+FSA, Part { II }
by Piotr Rudnicki
Received June 3, 1998
521. SFMASTR2
Another { \bf times } Macro Instruction
by Piotr Rudnicki
Received June 4, 1998
522. SFMASTR3
The { \bf for } (going up) Macro Instruction
by Piotr Rudnicki
Received June 4, 1998
523. JORDAN5D
Bounding Boxes for Special Sequences in ${\calE}^2$
by Yatsuka Nakamura and Adam Grabowski
Received June 8, 1998
524. EULER_2
Euler's Theorem and Small Fermat's Theorem
by Yoshinori Fujisawa, Yasushi Fuwa and Hidetaka Shimizu
Received June 10, 1998
525. GROUP_7
The Product of the Families of the Groups
by Artur Korni{\l}owicz
Received June 10, 1998
526. JORDAN7
On a Dividing Function of the Simple Closed Curve into
Segments
by Yatsuka Nakamura
Received June 16, 1998
527. SCM_HALT
Initialization Halting Concepts and Their Basic Properties of
SCM+FSA
by JingChao Chen and Yatsuka Nakamura
Received June 17, 1998
528. SCMBSORT
Bubble Sort on SCM+FSA
by JingChao Chen and Yatsuka Nakamura
Received June 17, 1998
529. WAYBEL19
The Lawson Topology
by Grzegorz Bancerek
Received June 21, 1998
530. WAYBEL20
Kernel Projections and Quotient Lattices
by Piotr Rudnicki
Received July 6, 1998
531. WAYBEL21
Lawson Topology in Continuous Lattices
by Grzegorz Bancerek
Received July 12, 1998
532. WAYBEL22
Representation theorem for free continuous lattices
by Piotr Rudnicki
Received July 21, 1998
533. GRAPH_4
Oriented Simple Chains Included in Oriented Chains
by Yatsuka Nakamura and Piotr Rudnicki
Received August 19, 1998
534. JGRAPH_1
Graph Theoretical Properties of Arcs in the Plane and
Fashoda Meet Theorem
by Yatsuka Nakamura
Received August 21, 1998
535. IDEA_1
Algebraic group on Fixed-length bit integer and its adaptation
to {IDEA} Cryptography
by Yasushi Fuwa and Yoshinori Fujisawa
Received September 7, 1998
536. TOPGRP_1
The Definition and Basic Properties of Topological Groups
by Artur Korni{\l}owicz
Received September 7, 1998
537. MSSUBLAT
The Correspondence Between Lattices of Subalgebras of
Universal Algebras and Many Sorted Algebras
by Adam Naumowicz and Agnieszka Julia Marasik
Received September 22, 1998
538. CONLAT_1
Introduction to Concept Lattices
by Christoph Schwarzweller
Received October 2, 1998
539. PARTIT1
A theory of partitions, { I }
by Shunichi Kobayashi and Kui Jia
Received October 5, 1998
540. BVFUNC_1
A Theory of Boolean Valued Functions and Partitions
by Shunichi Kobayashi and Kui Jia
Received October 22, 1998
541. SIN_COS
Trigonometric Functions and Existence of Circle Ratio
by Yuguang Yang and Yasunari Shidama
Received October 22, 1998
542. SPRECT_3
Some properties of special polygonal curves
by Andrzej Trybulec and Yatsuka Nakamura
Received October 22, 1998
543. VECTMETR
Real Linear-Metric Space and Isometric Functions
by Robert Milewski
Received November 3, 1998
544. YELLOW13
Introduction to Meet-Continuous Topological Lattices
by Artur Korni{\l}owicz
Received November 3, 1998
545. WAYBEL23
Bases of Continuous Lattices
by Robert Milewski
Received November 28, 1998
546. SCMRING1
The Construction of { \bf SCM } over Ring
by Artur Korni{\l}owicz
Received November 29, 1998
547. SCMRING2
The Basic Properties of { \bf SCM } over Ring
by Artur Korni{\l}owicz
Received November 29, 1998
548. BVFUNC_2
A Theory of Boolean Valued Functions and Quantifiers with
Respect to Partitions
by Shunichi Kobayashi and Yatsuka Nakamura
Received December 21, 1998
549. BVFUNC_3
Predicate Calculus for Boolean Valued Functions, { I }
by Shunichi Kobayashi and Yatsuka Nakamura
Received December 21, 1998
550. PEPIN
Public-Key Cryptography and Pepin's Test for the Primality
of Fermat Numbers
by Yoshinori Fujisawa , Yasushi Fuwa and Hidetaka Shimizu
Received December 21, 1998
551. HEYTING2
Lattice of Substitutions Is a Heyting Algebra
by Adam Grabowski
Received December 31, 1998
552. JORDAN2C
Bounded Domains and Unbounded Domains
by Yatsuka Nakamura , Andrzej Trybulec and Czeslaw Bylinski
Received January 7, 1999
553. REVROT_1
Rotating and reversing. (Finite sequences)
by Andrzej Trybulec
Received January 21, 1999
554. SPRECT_4
On the components of the complement of a special polygonal curve
by Andrzej Trybulec and Yatsuka Nakamura
Received January 21, 1999
555. JORDAN8
Gauges
by Czes\law Byli\'nski
Received January 22, 1999
556. INT_3
The Ring of Integers, Euclidean Rings and Modulo Integers
by Christoph Schwarzweller
Received February 4, 1999
557. GATE_1
Logic Gates and Logical Equivalence of Adders
by Yatsuka Nakamura
Received February 4, 1999
558. FRECHET2
The Sequential Closure Operator In Sequential and Frechet Spaces
by Bart{\l}omiej Skorulski
Received February 13, 1999
559. BORSUK_3
Properties of the Product of Compact Topological Spaces
by Adam Grabowski
Received February 13, 1999
560. TOPREAL6
Compactness of the Bounded Closed Subsets of TOP-REAL 2
by Artur Korni{\l}owicz
Received February 19, 1999
561. HILBERT1
Hilbert Positive Propositional Calculus
by Adam Grabowski
Received February 20, 1999
562. TOPREAL7
Homeomorphism between [:TOP-REAL i,TOP-REAL j:] and TOP-REAL (i+j)
by Artur Korni{\l}owicz
Received February 21, 1999
563. FSCIRC_1
Full Subtracter Circuit. Part { I }
by Katsumi Wasaki and Noboru Endou
Received March 13, 1999
564. GATE_2
Correctness of Binary Counter Circuits
by Yuguang Yang , Wasaki Katsumi , Yasushi Fuwa and Yatsuka Nakamura
Received March 13, 1999
565. GATE_3
Correctness of Johnson Counter Circuits
by Yuguang Yang , Wasaki Katsumi , Yasushi Fuwa and Yatsuka Nakamura
Received March 13, 1999
566. INTEGRA1
The Definition of Riemann Definite Integral and some Related Lemmas
by Noboru Endou and Artur Korni{\l}owicz
Received March 13, 1999
567. SIN_COS2
Properties of Trigonometric Function
by Takashi Mitsuishi and Yuguang Yang
Received March 13, 1999
568. BVFUNC_4
Predicate Calculus for Boolean Valued Functions, II
by Shunichi Kobayashi and Yatsuka Nakamura
Received March 13, 1999
569. BVFUNC_5
Propositional Calculus for Boolean Valued Functions, I
by Shunichi Kobayashi and Yatsuka Nakamura
Received March 13, 1999
570. BVFUNC_6
Propositional Calculus for Boolean Valued Functions, II
by Shunichi Kobayashi and Yatsuka Nakamura
Received March 13, 1999
571. SCMISORT
Insert Sort on SCM+FSA
by JingChao Chen
Received March 13, 1999
572. GATE_4
Correctness of a Cyclic Redundancy Check Code Generator
by Yuguang Yang, Katsumi Wasaki, Yasushi Fuwa and Yatsuka Nakamura
Received April 16, 1999
573. HILBERT2
Defining by structural induction in the positive propositional language
by Andrzej Trybulec
Received April 23, 1999
574. GOBRD13
Some Properties of Cells on Go Board
by Czes{\l}aw Byli\'nski
Received April 23, 1999
575. BVFUNC_7
Propositional Calculus For Boolean Valued Functions, III
by Shunichi Kobayashi
Received April 23, 1999
Has been removed on November 10, 2013
576. BVFUNC_8
Propositional Calculus For Boolean Valued Functions, IV
by Shunichi Kobayashi
Received April 23, 1999
Has been removed on November 10, 2013
577. GENEALG1
Basic Properties of Genetic Algorithm
by Akihiko Uchibori and Noboru Endou
Received April 24, 1999
578. BVFUNC_9
Propositional Calculus for Boolean Valued Functions, { V }
by Shunichi Kobayashi
Received May 5, 1999
Has been removed on November 10, 2013
579. GOBRD14
Properties of Left-, and Right Components
by Artur Korni{\l}owicz
Received May 5, 1999
580. LATTICE6
Noetherian Lattices
by Christoph Schwarzweller
Received June 9, 1999
581. SCMPDS_1
A Small Computer Model with Push-Down Stack
by JingChao Chen
Received June 15, 1999
582. SCMPDS_2
The SCMPDS Computer and the Basic Semantics of Its Instructions
by JingChao Chen
Received June 15, 1999
583. SCMPDS_3
Computation and Program Shift in the SCMPDS Computer
by JingChao Chen
Received June 15, 1999
584. SCMPDS_4
The Construction and shiftability of Program Blocks for SCMPDS
by JingChao Chen
Received June 15, 1999
585. SCMPDS_5
Computation of Two Consecutive Program Blocks for SCMPDS
by JingChao Chen
Received June 15, 1999
586. SCMPDS_6
The Construction and Computation of Conditional Statements for SCMPDS
by JingChao Chen
Received June 15, 1999
587. SCMP_GCD
Recursive Euclide Algorithm
by JingChao Chen
Received June 15, 1999
588. WAYBEL24
Scott-Continuous Functions, Part II
by Adam Grabowski
Received June 22, 1999
589. YELLOW14
Some Properties of Isomorphism between Relational Structures.
On the Product of Topological Spaces
by Jaros{\l}aw Gryko and Artur Korni{\l}owicz
Received June 22, 1999
590. JORDAN9
Cages, external aproximation of Jordan's curve
by Czes{\l}aw Byli\'nski and Mariusz \.Zynel
Received June 22, 1999
591. YELLOW15
Components and Basis of Topological Spaces
by Robert Milewski
Received June 22, 1999
592. JORDAN10
Properties of the External Approximation of Jordan's Curve
by Artur Korni{\l}owicz
Received June 24, 1999
593. IRRAT_1
Irrationality of e
by Freek Wiedijk
Received July 2, 1999
594. WAYBEL25
Injective Spaces, Part { II }
by Artur Korni{\l}owicz and Jaros{\l}aw Gryko
Received July 3, 1999
595. BVFUNC10
Propositional Calculus for Boolean Valued Functions, VI
by Shunichi Kobayashi
Received July 14, 1999
Has been removed on November 10, 2013
596. BVFUNC11
Predicate Calculus for Boolean Valued Functions, III
by Shunichi Kobayashi and Yatsuka Nakamura
Received July 14, 1999
597. CONLAT_2
A Characterization of Concept Lattices; Dual Concept Lattices
by Christoph Schwarzweller
Received August 17, 1999
598. BVFUNC12
Predicate Calculus for Boolean Valued Functions, IV
by Shunichi Kobayashi and Yatsuka Nakamura
Received August 17, 1999
Has been removed on July 5, 2005
599. BVFUNC13
Predicate Calculus for Boolean Valued Functions, V
by Shunichi Kobayashi and Yatsuka Nakamura
Received August 17, 1999
Has been removed on July 12, 2010
600. RADIX_1
Definitions of Radix-2k Signed-Digit number and its adder algorithm
by Yoshinori Fujisawa and Yasushi Fuwa
Received September 7, 1999
601. YELLOW16
Retracts and Inheritance
by Grzegorz Bancerek
Received September 7, 1999
602. ALGSPEC1
Technical Preliminaries to Algebraic Specifications
by Grzegorz Bancerek
Received September 7, 1999
603. POLYNOM1
Multivariate polynomials with arbitrary number of variables
by Piotr Rudnicki and Andrzej Trybulec
Received September 22, 1999
604. WAYBEL26
Continuous Lattices of Maps between T$_0$ Spaces
by Grzegorz Bancerek
Received September 24, 1999
605. BVFUNC14
Predicate Calculus for Boolean Valued Functions, { VI }
by Shunichi Kobayashi
Received October 19, 1999
606. BVFUNC15
Predicate Calculus for Boolean Valued Functions, { VII }
by Shunichi Kobayashi
Received October 19, 1999
Has been removed on February 27, 2003
607. BVFUNC16
Predicate Calculus for Boolean Valued Functions, { VIII }
by Shunichi Kobayashi
Received November 4, 1999
Has been removed on April 30, 2002
608. BVFUNC17
Predicate Calculus for Boolean Valued Functions, IX
by Shunichi Kobayashi
Received November 4, 1999
Has been removed on April 10, 2002
609. ASYMPT_0
Asymptotic notation. Part I: Theory
by Richard Krueger, Piotr Rudnicki and Paul Shelley
Received November 4, 1999
610. ASYMPT_1
Asymptotic notation. Part II: Examples and Problems
by Richard Krueger, Piotr Rudnicki and Paul Shelley
Received November 4, 1999
611. BVFUNC18
Predicate Calculus for Boolean Valued Functions, { X }
by Shunichi Kobayashi
Received November 15, 1999
Has been removed on February 27, 2003
612. BVFUNC19
Predicate Calculus for Boolean Valued Functions, { XI }
by Shunichi Kobayashi
Received November 15, 1999
Has been removed on February 6, 2003
613. BVFUNC20
Four Variable Predicate Calculus for Boolean Valued Functions, (1)
by Shunichi Kobayashi
Received November 26, 1999
Has been removed on March 7, 2003
614. BVFUNC21
Four Variable Predicate Calculus for Boolean Valued Functions, (2)
by Shunichi Kobayashi
Received November 26, 1999
Has been removed on February 27, 2003
615. WAYBEL27
Function Spaces in the Category of Directed Suprema Preserving Maps
by Grzegorz Bancerek and Adam Naumowicz
Received November 26, 1999
616. CFUNCT_1
Property of Complex Functions
by Takashi Mitsuishi, Katsumi Wasaki and Yasunari Shidama
Received December 7, 1999
617. CFCONT_1
Property of Complex Sequence and Continuity of Complex
Function
by Takashi Mitsuishi , Katsumi Wasaki and Yasunari Shidama
Received December 7, 1999
618. INTEGRA2
Scalar Multiple of Riemann Definite Integral
by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
Received December 7, 1999
619. INTEGRA3
Darboux's Theorem
by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
Received December 7, 1999
620. BVFUNC22
Five Variable Predicate Calculus for Boolean Valued
Functions, ( 1 )
by Shunichi Kobayashi
Received December 27, 1999
Has been removed on July 12, 2004
621. BVFUNC23
Six Variable Predicate Calculus for Boolean Valued Functions, (1)
by Shunichi Kobayashi
Received December 27, 1999
Has been removed on January 4, 2006
622. SCMPDS_7
The Construction and Computation of For-loop Programs for
SCMPDS
by JingChao Chen and Piotr Rudnicki
Received December 27, 1999
623. BVFUNC24
Predicate Calculus for Boolean Valued Functions, (12)
by Shunichi Kobayashi
Received December 28, 1999
Has been removed on December 19, 2008
624. WAYBEL28
Lim-inf Convergence
by Bart{\l}omiej Skorulski
Received January 6, 2000
625. WAYBEL29
The Characterization of Continuity of Topologies
by Grzegorz Bancerek and Adam Naumowicz
Received January 6, 2000
626. WAYBEL30
Meet Continuous Lattices Revisited
by Artur Korni{\l}owicz
Received January 6, 2000
627. WAYBEL31
Weights of Continuous Lattices
by Robert Milewski
Received January 6, 2000
628. LATTICE7
Representation Theorem For Finite Distributive Lattices
by Marek Dudzicz
Received January 6, 2000
629. COMPLFLD
The Field of Complex Numbers
by Anna Justyna Milewska
Received January 18, 2000
630. INTEGRA4
Integrability of Bounded Total Functions
by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
Received February 1, 2000
631. RADIX_2
High-speed algorithms for RSA cryptograms
by Yasushi Fuwa and Yoshinori Fujisawa
Received February 1, 2000
632. INTEGRA5
Definition of Integrability for Partial Functions from REAL
to REAL and Integrability for Continuous Functions
by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
Received March 23, 2000
633. RFUNCT_4
Introduction to Several Concepts of Convexity and
Semicontinuity for Function from REAL to REAL
by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
Received March 23, 2000
634. AMISTD_1
Standard Ordering of Instruction Locations
by Andrzej Trybulec , Piotr Rudnicki and Artur Korni{\l}owicz
Received April 14, 2000
635. AMISTD_2
On the Composition of Macro Instructions of Standard
Computers
by Artur Korni{\l}owicz
Received April 14, 2000
636. SCMRING3
The Properties of Instructions of { \bf SCM } over Ring
by Artur Korni{\l}owicz
Received April 14, 2000
637. CARD_FIL
Basic facts about inaccessible and measurable cardinals
by Josef Urban
Received April 14, 2000
638. POLYNOM2
Evaluation of Multivariate Polynomials
by Christoph Schwarzweller and Andrzej Trybulec
Received April 14, 2000
639. POLYNOM3
The Ring of Polynomials
by Robert Milewski
Received April 17, 2000
640. POLYEQ_1
Solving Roots of Polynomial Equations of Degree 2 and 3
with Real Coefficients
by Xiquan Liang
Received May 18, 2000
641. FUZZY_1
Concept of Fuzzy Set and Membership Function and Basic
Properties of Fuzzy Set Operation
by Takashi Mitsuishi , Noboru Endou and Yasunari Shidama
Received May 18, 2000
642. FUZZY_2
Basic Properties of Fuzzy Set Operation and Membership
Function
by Takashi Mitsuishi , Katsumi Wasaki and Yasunari Shidama
Received May 22, 2000
643. HAHNBAN1
Hahn Banach Theorem in the Vector Space over the Field of
Complex Numbers
by Anna Justyna Milewska
Received May 23, 2000
644. YELLOW17
The Tichonov Theorem
by Bart{\l}omiej Skorulski
Received May 23, 2000
645. WAYBEL32
On the Order-consistent Topology of Complete and Uncomplete
Lattices
by Ewa Gr\c{a}dzka
Received May 23, 2000
646. PENCIL_1
On Segre's Product of Partial Line Spaces
by Adam Naumowicz
Received May 29, 2000
647. POLYNOM4
Evaluation of Polynomials
by Robert Milewski
Received June 7, 2000
648. SCMPDS_8
The Construction and Computation of While-loop Programs for
SCMPDS
by JingChao Chen
Received June 14, 2000
649. SCPISORT
Insert Sort on SCMPDS
by JingChao Chen
Received June 14, 2000
650. SCPQSORT
Quick Sort on SCMPDS
by JingChao Chen
Received June 14, 2000
651. SCPINVAR
Justifying the Correctness of Fibonacci Sequence and Euclide
Algorithm by Loop Invariant
by JingChao Chen
Received June 14, 2000
652. ORDERS_4
On the Isomorphism Between Finite Chains
by Marta Pruszy\'nska and Marek Dudzicz
Received June 29, 2000
653. LATTICE8
J\'onsson Theorem about Representation of Modular Lattices
by Mariusz {\L}api\'nski
Received June 29, 2000
654. HILBERT3
The canonical formulae
by Andrzej Trybulec
Received July 4, 2000
655. HEYTING3
The Incompleteness of the Lattice of Substitutions
by Adam Grabowski
Received July 17, 2000
656. COMPTRIG
Trigonometric Form of Complex Numbers
by Robert Milewski
Received July 21, 2000
657. POLYNOM5
Fundamental Theorem of Algebra
by Robert Milewski
Received August 21, 2000
658. FINSEQ_7
On Replace Function and Swap Function for Finite Sequences
by Hiroshi Yamazaki , Yoshinori Fujisawa and Yatsuka Nakamura
Received August 28, 2000
659. GATE_5
Correctness of the High Speed Array Multiplier Circuits
by Hiroshi Yamazaki and Katsumi Wasaki
Received August 28, 2000
660. JCT_MISC
Miscellaneous { I }
by Andrzej Trybulec
Received August 28, 2000
661. CARD_LAR
Mahlo and inaccessible cardinals
by Josef Urban
Received August 28, 2000
662. EXTREAL1
Basic Properties of Extended Real Numbers
by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
Received September 7, 2000
663. MESFUNC1
Definitions and Basic Properties of Measurable Functions
by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
Received September 7, 2000
664. JORDAN1A
Gauges and Cages
by Artur Korni{\l}owicz, Robert Milewski, Adam Naumowicz and
Andrzej Trybulec
Received September 12, 2000
665. EXTREAL2
Some Properties of Extended Real Numbers Operations: absolute
value, min and max
by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
Received September 15, 2000
Has been removed on November 10, 2013
666. FUZZY_3
Concept of Fuzzy Relation and Basic Properties of Its
Operation
by Takashi Mitsuishi , Katsumi Wasaki and Yasunari Shidama
Received September 15, 2000
Has been removed on November 22, 2007
667. MESFUNC2
Measurability of Extended Real Valued Functions
by Noboru Endou , Katsumi Wasaki and Yasunari Shidama
Received October 6, 2000
668. JORDAN1B
Some Properties of Cells and Arcs
by Robert Milewski , Andrzej Trybulec , Artur Korni{\l}owicz and Adam Naumowicz
Received October 6, 2000
669. FINTOPO2
Formal topological spaces
by Gang Liu , Yasushi Fuwa and Masayoshi Eguchi
Received October 13, 2000
670. JORDAN1C
Some Properties of Cells and Gauges
by Adam Grabowski , Artur Korni{\l}owicz and Andrzej Trybulec
Received October 13, 2000
671. SPRECT_5
Again on the Order on a Special Polygon
by Andrzej Trybulec and Yatsuka Nakamura
Received October 16, 2000
672. JORDAN1D
Gauges and Cages. { P } art { II }
by Artur Korni{\l}owicz and Robert Milewski
Received November 6, 2000
673. BINOM
The Binomial Theorem for Algebraic Structures
by Christoph Schwarzweller
Received November 20, 2000
674. IDEAL_1
Ring Ideals
by Jonathan Backer , Piotr Rudnicki and Christoph Schwarzweller
Received November 20, 2000
675. HILBASIS
Hilbert Basis Theorem
by Jonathan Backer and Piotr Rudnicki
Received November 27, 2000
676. DYNKIN
Dynkin's Lemma in Measure Theory
by Franz Merkl
Received November 27, 2000
677. TAXONOM1
Lower Tolerance. {P}reliminaries to {W}roclaw Taxonomy
by Mariusz Giero and Roman Matuszewski
Received December 5, 2000
678. YELLOW18
Concrete Categories
by Grzegorz Bancerek
Received January 12, 2001
679. PARTIT_2
Classes of Independent Partitions
by Andrzej Trybulec
Received February 14, 2001
680. URYSOHN2
Some Properties of Dyadic Numbers and Intervals
by J\'ozef Bia{\l}as and Yatsuka Nakamura
Received February 16, 2001
681. URYSOHN3
Urysohn Lemma
by J\'ozef Bia{\l}as and Yatsuka Nakamura
Received February 16, 2001
682. POLYALG1
The Algebra of Polynomials
by Ewa Gr\c{a}dzka
Received February 24, 2001
683. CIRCTRM1
Circuit Generated by Terms and Circuit Calculating Terms
by Grzegorz Bancerek
Received April 10, 2001
684. AMI_6
On the Instructions of { \bf SCM }
by Artur Korni{\l}owicz
Received May 8, 2001
685. AMI_7
Input and Output of Instructions
by Artur Korni{\l}owicz
Received May 8, 2001
MML Identifier has been changed into AMISTD_4
686. SCMFSA10
On the Instructions of { \bf SCM+FSA }
by Artur Korni{\l}owicz
Received May 8, 2001
687. ROBBINS1
Robbins Algebras vs. Boolean Algebras
by Adam Grabowski
Received June 12, 2001
688. FUZZY_4
Properties of Fuzzy Relation
by Noboru Endou , Takashi Mitsuishi and Keiji Ohkubo
Received June 25, 2001
689. JGRAPH_2
On Outside Fashoda Meet Theorem
by Yatsuka Nakamura
Received July 16, 2001
690. COMPUT_1
The set of primitive recursive functions
by Grzegorz Bancerek and Piotr Rudnicki
Received July 27, 2001
691. TURING_1
Introduction to Turing Machines
by Jingchao Chen and Yatsuka Nakamura
Received July 27, 2001
692. YELLOW19
On the characterizations of compactness
by Grzegorz Bancerek , Noboru Endou and Yuji Sakai
Received July 29, 2001
693. WAYBEL33
Compactness of Lim-inf Topology
by Grzegorz Bancerek and Noboru Endou
Received July 29, 2001
694. YELLOW20
Miscellaneous Facts about Functors
by Grzegorz Bancerek
Received July 31, 2001
695. YELLOW21
Categorial Background for Duality Theory
by Grzegorz Bancerek
Received August 1, 2001
696. MSAFREE3
Yet another construction of free algebra
by Grzegorz Bancerek and Artur Korni{\l}owicz
Received August 8, 2001
697. WAYBEL34
Duality Based on Galois Connection. Part I
by Grzegorz Bancerek
Received August 8, 2001
698. JORDAN1E
Upper and Lower Sequence of a Cage
by Robert Milewski
Received August 8, 2001
699. POLYNOM6
On polynomials with coefficients in a ring of polynomials
by Barbara Dzienis
Received August 10, 2001
700. PENCIL_2
On Cosets in Segre's Product of Partial Linear Spaces
by Adam Naumowicz
Received August 14, 2001
701. JGRAPH_3
On the Simple Closed Curve Property of the Circle and the
Fashoda Meet Theorem for It
by Yatsuka Nakamura
Received August 20, 2001
702. PYTHTRIP
Pythagorean triples
by Freek Wiedijk
Received August 26, 2001
703. JORDAN1F
Some Remarks on Finite Sequences on Go-boards
by Adam Naumowicz
Received August 29, 2001
704. JORDAN1G
Upper and Lower Sequence on the Cage. Part II
by Robert Milewski
Received September 28, 2001
705. AFINSQ_1
Zero Based Finite Sequences
by Tetsuya Tsunetou , Grzegorz Bancerek and Yatsuka Nakamura
Received September 28, 2001
706. JORDAN1H
More on External Approximation of a Continuum
by Andrzej Trybulec
Received October 7, 2001
707. TOPREAL8
More on the Finite Sequences on the Plane
by Andrzej Trybulec
Received October 25, 2001
708. POLYNOM7
More About Polynomials: Monomials and Constant Polynomials
by Christoph Schwarzweller
Received November 28, 2001
709. FSM_2
On state machines of calculating type
by Hisayoshi Kunimune , Grzegorz Bancerek and Yatsuka Nakamura
Received December 3, 2001
710. TAXONOM2
Hierarchies and Classifications of Sets
by Mariusz Giero
Received December 28, 2001
711. JGRAPH_4
Fan Homeomorphisms in the Plane
by Yatsuka Nakamura
Received January 8, 2002
712. RCOMP_2
Half Open Intervals in Real Numbers
by Yatsuka Nakamura
Received February 1, 2002
Has been removed on December 19, 2008
713. JORDAN1I
Some Remarks on Clockwise Oriented Sequences on Go-boards
by Adam Naumowicz and Robert Milewski
Received March 1, 2002
714. DICKSON
Dickson's lemma
by Gilbert Lee and Piotr Rudnicki
Received March 12, 2002
715. BAGORDER
On Ordering of Bags
by Gilbert Lee and Piotr Rudnicki
Received March 12, 2002
716. CIRCCMB2
Combining of Multi Cell Circuits
by Grzegorz Bancerek , Shin'nosuke Yamaguchi and Yasunari Shidama
Received March 22, 2002
717. FACIRC_2
Full Adder Circuit. Part { II }
by Grzegorz Bancerek , Shin'nosuke Yamaguchi and Katsumi Wasaki
Received March 22, 2002
718. JORDAN1J
Upper and Lower Sequence on the Cage, Upper and Lower Arcs
by Robert Milewski
Received April 5, 2002
719. FIB_NUM
Fibonacci Numbers
by Robert M. Solovay
Received April 19, 2002
720. JORDAN11
Preparing the Internal Approximations of Simple Closed Curves
by Andrzej Trybulec
Received May 21, 2002
721. JORDAN12
On the General Position of Special Polygons
by Mariusz Giero
Received May 27, 2002
722. JORDAN13
Introducing Spans
by Andrzej Trybulec
Received May 27, 2002
723. JGRAPH_5
General {F}ashoda {M}eet {T}heorem for Unit Circle
by Yatsuka Nakamura
Received June 24, 2002
724. JORDAN14
Properties of the Internal Approximation of {J}ordan's Curve
by Robert Milewski
Received June 27, 2002
725. CIRCCMB3
Preliminaries to Automatic Generation of Mizar Documentation for Circuits
by Grzegorz Bancerek and Adam Naumowicz
Received July 26, 2002
726. JORDAN15
Properties of the Upper and Lower Sequence on the Cage
by Robert Milewski
Received August 1, 2002
727. BORSUK_4
On the Decompositions of Intervals and Simple Closed Curves
by Adam Grabowski
Received August 7, 2002
728. JORDAN1K
On the Minimal Distance Between Set in {E}uclidean Space
by Andrzej Trybulec
Received August 19, 2002
729. TOPMETR3
Sequences of Metric Spaces and an Abstract Intermediate Value Theorem
by Yatsuka Nakamura and Andrzej Trybulec
Received September 11, 2002
730. JORDAN16
On the Decomposition of a Simple Closed Curve into Two Arcs
by Andrzej Trybulec and Yatsuka Nakamura
Received September 16, 2002
731. JORDAN17
The Ordering of Points on a Curve, Part {III}
by Artur Korni{\l}owicz
Received September 16, 2002
732. JORDAN18
The Ordering of Points on a Curve, Part {IV}
by Artur Korni{\l}owicz
Received September 16, 2002
733. OSALG_1
Order Sorted Algebras
by Josef Urban
Received September 19, 2002
734. OSALG_2
Subalgebras of a Order Sorted Algebra. {L}attice of Subalgebras
by Josef Urban
Received September 19, 2002
735. OSALG_3
Homomorphisms of Order Sorted Algebras
by Josef Urban
Received September 19, 2002
736. OSALG_4
Order Sorted Quotient Algebra
by Josef Urban
Received September 19, 2002
737. OSAFREE
Free Order Sorted Universal Algebra
by Josef Urban
Received September 19, 2002
738. RUSUB_1
Subspaces and Cosets of Subspace of Real Unitary Space
by Noboru Endou, Takashi Mitsuishi and Yasunari Shidama
Received October 9, 2002
739. RUSUB_2
Operations on Subspaces in Real Unitary Space
by Noboru Endou, Takashi Mitsuishi and Yasunari Shidama
Received October 9, 2002
740. RUSUB_3
Linear Combinations in Real Unitary Space
by Noboru Endou, Takashi Mitsuishi and Yasunari Shidama
Received October 9, 2002
741. RUSUB_4
Dimension of Real Unitary Space
by Noboru Endou, Takashi Mitsuishi and Yasunari Shidama
Received October 9, 2002
742. SIN_COS3
Trigonometric Functions on Complex Space
by Takashi Mitsuishi, Noboru Endou and Yasunari Shidama
Received October 10, 2002
743. RUSUB_5
Topology of Real Unitary Space
by Noboru Endou, Takashi Mitsuishi and Yasunari Shidama
Received October 25, 2002
744. ARMSTRNG
Armstrong's Axioms
by William W. Armstrong, Yatsuka Nakamura and Piotr Rudnicki
Received October 25, 2002
745. CONVEX1
Convex Sets and Convex Combinations
by Noboru Endou, Takashi Mitsuishi and Yasunari Shidama
Received November 5, 2002
746. VECTSP10
Quotient Vector Spaces and Functionals
by Jaros{\l}aw Kotowicz
Received November 5, 2002
747. BILINEAR
Bilinear Functionals in Vector Spaces
by Jaros{\l}aw Kotowicz
Received November 5, 2002
748. HERMITAN
Hermitan Functionals. {C}anonical Construction of Scalar Product in
Quotient Vector Space
by Jaros{\l}aw Kotowicz
Received November 12, 2002
749. NECKLACE
The Class of Series-Parallel Graphs, {I}
by Krzysztof Retel
Received November 18, 2002
750. TERMORD
Term Orders
by Christoph Schwarzweller
Received December 20, 2002
751. POLYRED
Polynomial Reduction
by Christoph Schwarzweller
Received December 20, 2002
752. PNPROC_1
Processes in {P}etri nets
by Grzegorz Bancerek, Mitsuru Aoki, Akio Matsumoto and Yasunari Shidama
Received December 20, 2002
753. RADIX_3
Improvement of Radix-$2^k$ Signed-Digit Number for High Speed Circuit
by Masaaki Niimura and Yasushi Fuwa
Received January 3, 2003
754. RADIX_4
High Speed Adder Algorithm with Radix-$2^k$ SD_Sub Number
by Masaaki Niimura and Yasushi Fuwa
Received January 3, 2003
755. GRAPH_5
The Underlying Principle of {D}ijkstra's Shortest Path Algorithm
by Jingchao Chen and Yatsuka Nakamura
Received January 7, 2003
756. HAUSDORF
On the {H}ausdorff Distance Between Compact Subsets
by Adam Grabowski
Received January 27, 2003
757. CHAIN_1
Chains on a Grating in Euclidean Space
by Freek Wiedijk
Received January 27, 2003
758. BHSP_5
Bessel's Inequality
by Hiroshi Yamazaki, Yasunari Shidama and Yatsuka Nakamura
Received January 30, 2003
759. BINARI_4
A Representation of Integers by Binary Arithmetics
and Addition of Integers
by Hisayoshi Kunimune and Yatsuka Nakamura
Received January 30, 2003
760. EUCLID_2
The Inner Product of Finite Sequences and of Points of $n$-dimensional
Topological Space
by Kanchun and Yatsuka Nakamura
Received February 3, 2003
761. POLYEQ_2
Solving Roots of Polynomial Equation of Degree 4 with Real Coefficients
by Xiquan Liang
Received February 3, 2003
762. WAYBEL35
Morphisms Into Chains, Part {I}
by Artur Korni{\l}owicz
Received February 6, 2003
763. BVFUNC25
Propositional Calculus for Boolean Valued Functions, {VII}
by Shunichi Kobayashi
Received February 6, 2003
764. OPOSET_1
Basic Notions and Properties of Orthoposets
by Markus Moschner
Received February 11, 2003
765. JGRAPH_6
General {F}ashoda Meet Theorem for Unit Circle and Square
by Yatsuka Nakamura
Received February 25, 2003
766. BHSP_6
On Some Properties of Real {H}ilbert Space, {I}
by Hiroshi Yamazaki, Yasumasa Suzuki, Takao Inou\'e and Yasunari Shidama
Received February 25, 2003
767. FSCIRC_2
Full Subtracter Circuit. Part {II}
by Shin'nosuke Yamaguchi, Grzegorz Bancerek and Katsumi Wasaki
Received February 25, 2003
768. GRAPHSP
Dijkstra's Shortest Path Algorithm
by Jing-Chao Chen
Received March 17, 2003
769. RSSPACE
Real Linear Space of Real Sequences
by Noboru Endou, Yasumasa Suzuki and Yasunari Shidama
Received April 3, 2003
770. RSSPACE2
Hilbert Space of Real Sequences
by Noboru Endou, Yasumasa Suzuki and Yasunari Shidama
Received April 3, 2003
771. INTPRO_1
Intuitionistic Propositional Calculus in the Extended Framework
with Modal Operator, Part I
by Takao Inou\'e
Received April 3, 2003
772. CONVEX2
Some Properties for Convex Combinations
by Noboru Endou, Yasumasa Suzuki and Yasunari Shidama
Received April 3, 2003
773. BHSP_7
On Some Properties of Real {H}ilbert Space, {II}
by Hiroshi Yamazaki, Yasumasa Suzuki, Takao Inou\'e and Yasunari Shidama
Received April 17, 2003
774. COMPLEX2
Inner Products and Angles of Complex Numbers
by Wenpai Chang, Yatsuka Nakamura and Piotr Rudnicki
Received May 29, 2003
775. EUCLID_3
Angle and Triangle in {E}uclidian Topological Space
by Akihiro Kubo and Yatsuka Nakamura
Received May 29, 2003
776. NECKLA_2
The Class of Series-Parallel Graphs, {II}
by Krzysztof Retel
Received May 29, 2003
777. GROEB_1
Characterization and Existence of {G}r\"obner Bases
by Christoph Schwarzweller
Received June 11, 2003
778. GROEB_2
Construction of {G}r\"obner bases. S-Polynomials and Standard
Representations
by Christoph Schwarzweller
Received June 11, 2003
779. BORSUK_5
On the Subcontinua of a Real Line
by Adam Grabowski
Received June 12, 2003
780. KURATO_1
On the {K}uratowski Closure-Complement Problem
by Lilla Krystyna Bagi\'nska and Adam Grabowski
Received June 12, 2003
781. CONVEX3
Convex Hull, Set of Convex Combinations and Convex Cone
by Noboru Endou and Yasunari Shidama
Received June 16, 2003
782. ROBBINS2
On the Two Short Axiomatizations of Ortholattices
by Wioletta Truszkowska and Adam Grabowski
Received June 28, 2003
783. CONVFUN1
Definition of Convex Function and {J}ensen's Inequality
by Grigory E. Ivanov
Received July 17, 2003
784. ABCMIZ_0
On semilattice structure of {M}izar types
by Grzegorz Bancerek
Received August 8, 2003
785. EUCLID_4
Lines in $n$-Dimensional Euclidean Spaces
by Akihiro Kubo
Received August 8, 2003
786. RSSPACE3
Banach Space of Absolute Summable Real Sequences
by Yasumasa Suzuki, Noboru Endou and Yasunari Shidama
Received August 8, 2003
787. EUCLID_5
Cross Products and Tripple Vector Products in 3-dimensional Euclidian Space
by Kanchun, Hiroshi Yamazaki and Yatsuka Nakamura
Received August 8, 2003
788. MATRIX_4
Calculation of Matrices of Field Elements. Part {I}
by Yatsuka Nakamura and Hiroshi Yamazaki
Received August 8, 2003
789. LFUZZY_0
Lattice of Fuzzy Sets
by Takashi Mitsuishi and Grzegorz Bancerek
Received August 12, 2003
790. KURATO_2
On the {K}uratowski Limit Operators
by Adam Grabowski
Received August 12, 2003
791. JORDAN_A
On the Segmentation of a Simple Closed Curve
by Andrzej Trybulec
Received August 18, 2003
792. MEMBERED
On the Sets Inhabited by Numbers
by Andrzej Trybulec
Received August 23, 2003
793. BINARI_5
On the Calculus of Binary Arithmetics
by Shunichi Kobayashi
Received August 23, 2003
Has been removed on June 30, 2010
794. SCMPDS_9
SCMPDS Is Not Standard
by Artur Korni{\l}owicz and Yasunari Shidama
Received September 27, 2003
795. JORDAN19
On the Upper and Lower Approximations of the Curve
by Robert Milewski
Received September 27, 2003
796. RFINSEQ2
Sorting Operators for Finite Sequences
by Yatsuka Nakamura
Received October 17, 2003
797. RADIX_5
Magnitude Relation Properties of Radix-$2^k$ SD Number
by Masaaki Niimura and Yasushi Fuwa
Received November 7, 2003
798. RADIX_6
High Speed Modulo Calculation Algorithm with Radix-$2^k$ SD Number
by Masaaki Niimura and Yasushi Fuwa
Received November 7, 2003
799. LFUZZY_1
Transitive Closure of Fuzzy Relations
by Takashi Mitsuishi and Grzegorz Bancerek
Received November 23, 2003
800. ROUGHS_1
Basic Properties of Rough Sets and Rough Membership Function
by Adam Grabowski
Received November 23, 2003
801. PRGCOR_1
Correctness of Non Overwriting Programs. {P}art {I}
by Yatsuka Nakamura
Received December 5, 2003
802. AMISTD_3
A Tree of Execution of a Macroinstruction
by Artur Korni{\l}owicz
Received December 10, 2003
803. LOPBAN_1
Banach Space of Bounded Linear Operators
by Yasunari Shidama
Received December 22, 2003
804. UPROOTS
Little {B}ezout Theorem (Factor Theorem)
by Piotr Rudnicki
Received December 30, 2003
805. UNIROOTS
Primitive Roots of Unity and Cyclotomic Polynomials
by Broderick Arneson and Piotr Rudnicki
Received December 30, 2003
806. WEDDWITT
Witt's Proof of the {W}edderburn Theorem
by Broderick Arneson, Matthias Baaz and Piotr Rudnicki
Received December 30, 2003
807. RSSPACE4
Banach Space of Bounded Real Sequences
by Yasumasa Suzuki
Received January 6, 2004
808. POLYEQ_3
Solving Complex Roots of Polynomial Equation of Degree 2 and 3 with
Complex Coefficients
by Yuzhong Ding and Xiquan Liang
Received January 26, 2004
809. CLVECT_1
Complex Linear Space and Complex Normed Space
by Noboru Endou
Received January 26, 2004
810. LOPBAN_2
The {B}anach Algebra of Bounded Linear Operators
by Yasunari Shidama
Received January 26, 2004
811. CSSPACE
Complex Linear Space of Complex Sequences
by Noboru Endou
Received January 26, 2004
812. JORDAN20
Behaviour of an Arc Crossing a Line
by Yatsuka Nakamura
Received January 26, 2004
813. FINTOPO3
Some Set Series in Finite Topological Spaces. {F}undamental Concepts
for Image Processing
by Masami Tanaka and Yatsuka Nakamura
Received January 26, 2004
814. LOPBAN_3
The Series on {B}anach Algebra
by Yasunari Shidama
Received February 3, 2004
815. SIN_COS4
Formulas And Identities of Trigonometric Functions
by Pacharapokin Chanapat, Kanchun and Hiroshi Yamazaki
Received February 3, 2004
816. NECKLA_3
The Class of Series-Parallel Graphs, {III}
by Krzysztof Retel
Received February 3, 2004
817. SCMRING4
Relocability for { \bf SCM } over Ring
by Artur Korni{\l}owicz and Yasunari Shidama
Received February 6, 2004
818. CLVECT_2
Convergent Sequences in Complex Unitary Space
by Noboru Endou
Received February 10, 2004
819. RECDEF_2
Recursive Definitions. {P}art {II}
by Artur Korni{\l}owicz
Received February 10, 2004
820. LOPBAN_4
The Exponential Function on {B}anach Algebra
by Yasunari Shidama
Received February 13, 2004
821. NAT_3
Fundamental {T}heorem of {A}rithmetic
by Artur Korni{\l}owicz and Piotr Rudnicki
Received February 13, 2004
822. CSSPACE2
Hilbert Space of Complex Sequences
by Noboru Endou
Received February 24, 2004
823. CSSPACE3
Banach Space of Absolute Summable Complex Sequences
by Noboru Endou
Received February 24, 2004
824. TAYLOR_1
The {T}aylor Expansions
by Yasunari Shidama
Received February 24, 2004
825. CLOPBAN1
Complex {B}anach Space of Bounded Linear Operators
by Noboru Endou
Received February 24, 2004
826. CSSPACE4
Complex Banach Space of Bounded Complex Sequences
by Noboru Endou
Received March 18, 2004
827. FINSEQ_8
Concatenation of Finite Sequences Reducing Overlapping Part and an
Argument of Separators of Sequential Files
by Hirofumi Fukura and Yatsuka Nakamura
Received March 18, 2004
828. CLVECT_3
Cauchy Sequence of Complex Unitary Space
by Yasumasa Suzuki and Noboru Endou
Received March 18, 2004
829. CFUNCDOM
Complex Valued Function's Space
by Noboru Endou
Received March 18, 2004
830. CLOPBAN2
Banach Algebra of Bounded Complex Linear Operators
by Noboru Endou
Received March 18, 2004
831. SIN_COS5
Formulas And Identities of Trigonometric Functions
by Yuzhong Ding and Xiquan Liang
Received March 18, 2004
832. POLYEQ_4
Solving the Roots of the Special Polynomial Equation with Real
Coefficients
by Yuzhong Ding and Xiquan Liang
Received March 18, 2004
833. BORSUK_6
Algebraic Properties of Homotopies
by Adam Grabowski and Artur Korni{\l}owicz
Received March 18, 2004
834. TOPALG_1
The Fundamental Group
by Artur Korni{\l}owicz, Yasunari Shidama and Adam Grabowski
Received March 18, 2004
835. NFCONT_1
The Continuous Functions on Normed Linear Spaces
by Takaya Nishiyama, Keiji Ohkubo and Yasunari Shidama
Received April 6, 2004
836. NFCONT_2
The Uniform Continuity of Functions on Normed Linear Spaces
by Takaya Nishiyama, Artur Korni{\l}owicz and Yasunari Shidama
Received April 6, 2004
837. CLOPBAN3
Series on Complex {B}anach Algebra
by Noboru Endou
Received April 6, 2004
838. CLOPBAN4
Exponential Function on Complex {B}anach Algebra
by Noboru Endou
Received April 6, 2004
839. TOPALG_2
The Fundamental Group of Convex Subspaces of TOP-REAL n
by Artur Korni{\l}owicz
Received April 20, 2004
840. TOPREAL9
Intersections of Intervals and Balls in TOP-REAL n
by Artur Korni{\l}owicz and Yasunari Shidama
Received May 10, 2004
841. FIB_NUM2
Some Properties of {F}ibonacci Numbers
by Magdalena Jastrz\c{e}bska and Adam Grabowski
Received May 10, 2004
842. HALLMAR1
The {H}all {M}arriage {T}heorem
by Ewa Romanowicz and Adam Grabowski
Received May 11, 2004
843. NDIFF_1
The Differentiable Functions on Normed Linear Spaces
by Hiroshi Imura, Morishige Kimura and Yasunari Shidama
Received May 24, 2004
844. FIB_NUM3
Lucas Numbers and Generalized {F}ibonacci Numbers
by Piotr Wojtecki and Adam Grabowski
Received May 24, 2004
845. LATSUM_1
The Operation of Addition of Relational Structures
by Katarzyna Romanowicz and Adam Grabowski
Received May 24, 2004
846. NAGATA_1
The {N}agata-Smirnov Theorem. {P}art {I}
by Karol P\c{a}k
Received May 31, 2004
847. GROUP_8
Properties of Groups
by Gijs Geleijnse and Grzegorz Bancerek
Received May 31, 2004
848. CATALAN1
Catalan Numbers
by Dorota Cz\c{e}stochowska and Adam Grabowski
Received May 31, 2004
849. SHEFFER1
Axiomatization of {B}oolean Algebras Based on Sheffer Stroke
by Violetta Kozarkiewicz and Adam Grabowski
Received May 31, 2004
850. SHEFFER2
Short {S}heffer Stroke-Based Single Axiom for {B}oolean Algebras
by Aneta {\L}ukaszuk and Adam Grabowski
Received May 31, 2004
851. NDIFF_2
Differentiable Functions on Normed Linear Spaces. {P}art {II}
by Hiroshi Imura, Yuji Sakai and Yasunari Shidama
Received June 4, 2004
852. PRGCOR_2
Logical Correctness of Vector Calculation Programs
by Takaya Nishiyama, Hirofumi Fukura and Yatsuka Nakamura
Received July 13, 2004
853. FINTOPO4
Continuous Mappings between Finite and One-Dimensional Finite Topological
Spaces
by Hiroshi Imura, Masami Tanaka and Yatsuka Nakamura
Received July 13, 2004
854. NAGATA_2
The {N}agata-Smirnov Theorem. {P}art {II}
by Karol P\c{a}k
Received July 22, 2004
855. TOPALG_3
On the Isomorphism of Fundamental Groups
by Artur Korni{\l}owicz
Received July 30, 2004
856. VFUNCT_2
Algebra of Complex Vector Valued Functions
by Noboru Endou
Received August 20, 2004
857. NCFCONT1
Continuous Functions on Real and Complex Normed Linear Spaces
by Noboru Endou
Received August 20, 2004
858. TOPALG_4
On the Fundamental Groups of Products of Topological Spaces
by Artur Korni{\l}owicz
Received August 20, 2004
859. SERIES_2
Partial Sum of Some Series
by Ming Liang and Yuzhong Ding
Received September 25, 2004
860. SUBSTUT1
Substitution in First-Order Formulas: Elementary Properties
by Patrick Braselmann and Peter Koepke
Received September 25, 2004
861. SUBLEMMA
Coincidence Lemma and Substitution Lemma
by Patrick Braselmann and Peter Koepke
Received September 25, 2004
862. SUBSTUT2
Substitution in First-Order Formulas -- Part II. {T}he Construction of
First-Order Formulas
by Patrick Braselmann and Peter Koepke
Received September 25, 2004
863. CALCUL_1
A Sequent Calculus for First-Order Logic
by Patrick Braselmann and Peter Koepke
Received September 25, 2004
864. CALCUL_2
Consequences of the Sequent Calculus
by Patrick Braselmann and Peter Koepke
Received September 25, 2004
865. HENMODEL
Equivalences of Inconsistency and {H}enkin Models
by Patrick Braselmann and Peter Koepke
Received September 25, 2004
866. GOEDELCP
G{\"o}del's Completeness Theorem
by Patrick Braselmann and Peter Koepke
Received September 25, 2004
867. BVFUNC26
Propositional Calculus for Boolean Valued Functions, {VIII}
by Shunichi Kobayashi
Received September 25, 2004
Has been removed on November 10, 2013
868. HOLDER_1
H\"older's Inequality and {M}inkowski's Inequality
by Yasumasa Suzuki
Received September 25, 2004
869. LP_SPACE
The Banach Space $l^p$
by Yasumasa Suzuki
Received September 25, 2004
870. MESFUNC3
Lebesgue Integral of Simple Valued Function
by Yasunari Shidama and Noboru Endou
Received September 25, 2004
871. SIN_COS6
Inverse Trigonometric Functions Arcsin and Arccos
by Artur Korni{\l}owicz and Yasunari Shidama
Received September 25, 2004
872. JORDAN21
On Some Points of a Simple Closed Curve
by Artur Korni{\l}owicz
Received October 6, 2004
873. JORDAN22
On Some Points of a Simple Closed Curve. {P}art {II}
by Artur Korni{\l}owicz and Adam Grabowski
Received October 6, 2004
874. NCFCONT2
Uniform Continuity of Functions on Normed Complex Linear Spaces
by Noboru Endou
Received October 6, 2004
875. RLTOPSP1
Introduction to Real Linear Topological Spaces
by Czes{\l}aw Byli\'nski
Received October 6, 2004
876. TOPREALA
Some Properties of Rectangles on the Plane
by Artur Korni{\l}owicz and Yasunari Shidama
Received October 18, 2004
877. TOPREALB
Some Properties of Circles on the Plane
by Artur Korni{\l}owicz and Yasunari Shidama
Received October 18, 2004
878. PENCIL_3
On the Characterization of Collineations of the Segre Product of Strongly
Connected Partial Linear Spaces
by Adam Naumowicz
Received October 18, 2004
879. PENCIL_4
Spaces of Pencils, {G}rassmann Spaces, and Generalized {V}eronese
Spaces
by Adam Naumowicz
Received November 8, 2004
880. TOPGEN_1
On the Boundary and Derivative of a Set
by Adam Grabowski
Received November 8, 2004
881. GROEB_3
Construction of {G}r\"obner Bases: Avoiding S-Polynomials -- Buchberger's
First Criterium
by Christoph Schwarzweller
Received December 10, 2004
882. MATRIX_5
A Theory of Matrices of Complex Elements
by Wenpai Chang, Hiroshi Yamazaki and Yatsuka Nakamura
Received December 10, 2004
883. TOPGEN_2
On the characteristic and weight of a topological space
by Grzegorz Bancerek
Received December 10, 2004
884. TOPGEN_3
On constructing topological spaces and Sorgenfrey line
by Grzegorz Bancerek
Received December 10, 2004
885. PARTFUN3
On the Real Valued Functions
by Artur Korni{\l}owicz
Received December 10, 2004
886. ROBBINS3
Formalization of Ortholattices via Orthoposets
by Adam Grabowski and Markus Moschner
Received December 28, 2004
887. JGRAPH_7
Fashoda Meet Theorem for Rectangles
by Yatsuka Nakamura and Andrzej Trybulec
Received January 3, 2005
888. MATHMORP
Preliminaries to Mathematical Morphology and Its Properties
by Yuzhong Ding and Xiquan Liang
Received January 7, 2005
889. JORDAN23
Subsequences of Almost, Weakly and Poorly One-to-one Finite Sequences
by Robert Milewski
Received February 1, 2005
890. GLIB_000
Alternative Graph Structures
by Gilbert Lee and Piotr Rudnicki
Received February 22, 2005
891. GLIB_001
Walks in a Graph
by Gilbert Lee
Received February 22, 2005
892. GLIB_002
Trees: Connected, Acyclic Graphs
by Gilbert Lee
Received February 22, 2005
893. GLIB_003
Weighted and Labeled Graphs
by Gilbert Lee
Received February 22, 2005
894. GLIB_004
Proof of Dijkstra's Shortest Path Algorithm & Prim's Minimum Spanning
Tree Algorithm
by Gilbert Lee and Piotr Rudnicki
Received February 22, 2005
895. GLIB_005
Proof of Ford/Fulkerson's Maximum Network Flow Algorithm
by Gilbert Lee
Received February 22, 2005
896. RCOMP_3
Properties of Connected Subsets of the Real Line
by Artur Korni{\l}owicz
Received February 22, 2005
897. TOPALG_5
The Fundamental Group of the Circle
by Artur Korni{\l}owicz
Received February 22, 2005
898. BROUWER
Brouwer Fixed Point Theorem for Disks on the Plane
by Artur Korni{\l}owicz and Yasunari Shidama
Received February 22, 2005
899. STIRL2_1
Stirling Numbers of the Second Kind
by Karol P\c{a}k
Received March 15, 2005
900. SETLIM_1
Limit of Sequence of Subsets
by Bo Zhang, Hiroshi Yamazaki and Yatsuka Nakamura
Received March 15, 2005
901. ISOMICHI
The Properties of Supercondensed Sets, Subcondensed Sets and Condensed Sets
by Magdalena Jastrz\c{e}bska and Adam Grabowski
Received March 31, 2005
902. RELSET_2
Properties of First and Second Order Cutting of Binary Relations
by Krzysztof Retel
Received April 25, 2005
903. COMPLSP2
The Inner Product and Conjugate of Finite Sequences of Complex Numbers
by Wenpai Chang, Hiroshi Yamazaki and Yatsuka Nakamura
Received April 25, 2005
904. RINFSUP1
Inferior Limit and Superior Limit of Sequences of Real Numbers
by Bo Zhang, Hiroshi Yamazaki and Yatsuka Nakamura
Received April 29, 2005
905. SIN_COS7
Formulas And Identities of Inverse Hyperbolic Functions
by Fuguo Ge, Xiquan Liang and Yuzhong Ding
Received May 24, 2005
906. EUCLIDLP
Lines on Planes in $n$-Dimensional Euclidean Spaces
by Akihiro Kubo
Received May 24, 2005
907. CARD_FIN
Cardinal Numbers and Finite Sets
by Karol P\c{a}k
Received May 24, 2005
908. SETLIM_2
Some Equations Related to the Limit of Sequence of Subsets
by Bo Zhang, Hiroshi Yamazaki and Yatsuka Nakamura
Received May 24, 2005
909. SERIES_3
On the Partial Product of Series and Related Basic Inequalities
by Fuguo Ge and Xiquan Liang
Received July 6, 2005
910. FINTOPO5
Homeomorphism between Finite Topological Spaces, Two-Dimensional Lattice
Spaces and a Fixed Point Theorem
by Masami Tanaka, Hiroshi Imura and Yatsuka Nakamura
Received July 6, 2005
911. TAYLOR_2
The {M}aclaurin Expansions
by Akira Nishino and Yasunari Shidama
Received July 6, 2005
912. FDIFF_4
Several Differentiable Formulas of Special Functions
by Yan Zhang and Xiquan Liang
Received July 6, 2005
913. PROB_3
Set Sequences and Monotone Class
by Bo Zhang, Hiroshi Yamazaki and Yatsuka Nakamura
Received August 12, 2005
914. FILEREC1
A Theory of Sequential Files
by Hirofumi Fukura and Yatsuka Nakamura
Received August 12, 2005
915. CIRCLED1
Circled Sets, Circled Hull, and Circled Family
by Fahui Zhai, Jianbing Cao and Xiquan Liang
Received August 30, 2005
916. TOPGEN_4
On the {B}orel Families of Subsets of Topological Spaces
by Adam Grabowski
Received August 30, 2005
917. MESFUNC4
Linearity of {L}ebesgue Integral of Simple Valued Function
by Noboru Endou and Yasunari Shidama
Received September 14, 2005
918. JGRAPH_8
The {F}ashoda Meet Theorem for Continuous Mappings
by Yatsuka Nakamura, Andrzej Trybulec and Artur Korni{\l}owicz
Received September 14, 2005
919. TIETZE
Tietze {E}xtension {T}heorem
by Artur Korni{\l}owicz, Grzegorz Bancerek and Adam Naumowicz
Received September 14, 2005
920. JORDAN24
Homeomorphisms of {J}ordan Curves
by Adam Naumowicz and Grzegorz Bancerek
Received September 15, 2005
921. JORDAN
Jordan's Curve Theorem
by Artur Korni{\l}owicz
Received September 15, 2005
922. MATRIXC1
The Inner Product and Conjugate of Matrix of Complex Numbers
by Wenpai Chang, Hiroshi Yamazaki and Yatsuka Nakamura
Received October 10, 2005
923. SERIES_4
Partial Sum and Partial Product of Some Series
by Jianbing Cao, Fahui Zhai and Xiquan Liang
Received November 7, 2005
924. FDIFF_5
Some Differentiable Formulas of Special Functions
by Jianbing Cao, Fahui Zhai and Xiquan Liang
Received November 7, 2005
925. SIN_COS8
Formulas and Identities of Hyperbolic Functions
by Pacharapokin Chanapat and Hiroshi Yamazaki
Received November 7, 2005
926. TOPGEN_5
Niemytzki Plane -- an Example of {T}ychonoff Space Which Is Not $T_4$
by Grzegorz Bancerek
Received November 7, 2005
927. SERIES_5
On the Partial Product and Partial Sum of Series and Related Basic
Inequalities
by Fuguo Ge and Xiquan Liang
Received November 23, 2005
928. FDIFF_6
Several Differentiable Formulas of Special Functions -- Part {II}
by Yan Zhang, Bo Li and Xiquan Liang
Received November 23, 2005
929. BINARI_6
On the Calculus of Binary Arithmetics, Part {II}
by Shunichi Kobayashi
Received November 23, 2005
Has been removed on November 30, 2006
930. PROB_4
The Relevance of Measure and Probability and Definition of Completeness
of Probability
by Bo Zhang, Hiroshi Yamazaki and Yatsuka Nakamura
Received November 23, 2005
931. MATRIX_6
Some Properties Of Some Special Matrices
by Xiaopeng Yue, Xiquan Liang and Zhongpin Sun
Received December 7, 2005
932. GFACIRC1
Generalized Full Adder Circuits (GFAs). {P}art {I}
by Shin'nosuke Yamaguchi, Katsumi Wasaki and Nobuhiro Shimoi
Received December 7, 2005
933. RING_1
Quotient Rings
by Artur Korni{\l}owicz
Received December 7, 2005
934. REAL_NS1
Completeness of the Real {E}uclidean Space
by Noboru Endou and Yasunari Shidama
Received December 28, 2005
935. MATRIX_7
Determinant of Some Matrices of Field Elements
by Yatsuka Nakamura
Received January 4, 2006
936. MATRIX_8
Some Properties Of Some Special Matrices, Part {II}
by Xiaopeng Yue, Dahai Hu, Xiquan Liang and Zhongpin Sun
Received January 4, 2006
937. MATRIX_9
On the Permanent of a Matrix
by Ewa Romanowicz and Adam Grabowski
Received January 4, 2006
938. MATRIXR1
A Theory of Matrices of Real Elements
by Yatsuka Nakamura, Nobuyuki Tamura and Wenpai Chang
Received February 20, 2006
939. MOEBIUS1
On the Properties of the {M}\"obius Function
by Magdalena Jastrz\c{e}bska and Adam Grabowski
Received March 21, 2006
940. FDIFF_7
Several Differentiation Formulas of Special Functions -- Part {III}
by Bo Li, Yan Zhang and Xiquan Liang
Received March 22, 2006
941. NAT_4
Pocklington's Theorem and {B}ertrand's Postulate
by Marco Riccardi
Received May 17, 2006
942. MESFUNC5
Integral of Measurable Function
by Noboru Endou and Yasunari Shidama
Received May 24, 2006
943. REAL_3
Simple Continued Fractions and Their Convergents
by Bo Li, Yan Zhang and Artur Korni{\l}owicz
Received August 18, 2006
944. CHORD
Chordal Graphs
by Broderick Arneson and Piotr Rudnicki
Received August 18, 2006
945. FINTOPO6
Connectedness and Continuous Sequences in Finite Topological Spaces
by Yatsuka Nakamura
Received August 18, 2006
946. MATRPROB
The Definition of Finite Sequences and Matrices of Probability, and
Addition of Matrices of Real Elements
by Bo Zhang and Yatsuka Nakamura
Received August 18, 2006
947. FDIFF_8
Several Differentiation Formulas of Special Functions -- Part {IV}
by Bo Li and Peng Wang
Received September 29, 2006
948. DIFF_1
Difference and Difference Quotient
by Bo Li, Yan Zhang and Xiquan Liang
Received September 29, 2006
949. POLYNOM8
Multiplication of Polynomials using {D}iscrete {F}ourier {T}ransformation
by Krzysztof Treyderowski and Christoph Schwarzweller
Received October 12, 2006
950. MATRIX10
Some Special Matrices of Real Elements and Their Properties
by Xiquan Liang, Fuguo Ge and Xiaopeng Yue
Received October 19, 2006
951. HURWITZ
Schur's Theorem on the Stability of Networks
by Agnieszka Rowi\'nska-Schwarzweller and Christoph Schwarzweller
Received October 19, 2006
952. MESFUNC6
Integral of Real-valued Measurable Function
by Yasunari Shidama and Noboru Endou
Received October 27, 2006
953. CATALAN2
The {C}atalan Numbers. {P}art {II}
by Karol P\c{a}k
Received October 31, 2006
954. QUATERNI
The Quaternion Numbers
by Xiquan Liang and Fuguo Ge
Received November 14, 2006
955. MODELC_1
Model Checking, Part {I}
by Kazuhisa Ishida
Received November 14, 2006
956. LEXBFS
Recognizing Chordal Graphs: Lex BFS and MCS
by Broderick Arneson and Piotr Rudnicki
Received November 17, 2006
957. INTEGRA6
Integrability and the Integral of Partial Functions from $\Bbb R$ into
$\Bbb R$
by Noboru Endou, Yasunari Shidama and Masahiko Yamazaki
Received November 17, 2006
958. NORMSP_2
Baire's Category Theorem and Some Spaces Generated from Real Normed Space
by Noboru Endou, Yasunari Shidama and Katsumasa Okamura
Received November 21, 2006
959. NUMERAL1
On the Representation of Natural Numbers in Positional Numeral Systems
by Adam Naumowicz
Received December 31, 2006
960. BCIALG_1
Several Classes of {BCI}-algebras and Their Properties
by Yuzhong Ding
Received February 23, 2007
961. FLANG_1
Formal Languages -- Concatenation and Closure
by Micha{\l} Trybulec
Received March 9, 2007
962. MATRIX11
Basic Properties of Determinants of Square Matrices over a Field
by Karol P\c{a}k
Received March 21, 2007
963. COMBGRAS
Combinatorial {G}rassmannians
by Andrzej Owsiejczuk
Received April 16, 2007
964. GROUP_9
The {J}ordan-H\"older Theorem
by Marco Riccardi
Received April 20, 2007
965. FLANG_2
Regular Expression Quantifiers -- $m$ to $n$ Occurrences
by Micha{\l} Trybulec
Received June 6, 2007
966. INTEGRA7
Riemann Indefinite Integral of Functions of Real Variable
by Yasunari Shidama, Noboru Endou, Katsumi Wasaki and Katuhiko Kanazashi
Received June 6, 2007
967. PDIFF_1
Partial Differentiation on Normed Linear Spaces $ {\cal R}^n$
by Noboru Endou, Yasunari Shidama and Keiichi Miyajima
Received June 6, 2007
968. FDIFF_9
Several Differentiation Formulas of Special Functions -- Part {V}
by Peng Wang and Bo Li
Received July 9, 2007
969. PRVECT_2
The Product Space of Real Normed Spaces and Its Properties
by Noboru Endou, Yasunari Shidama and Keiichi Miyajima
Received July 9, 2007
970. AOFA_000
Mizar Analysis of Algorithms: Preliminaries
by Grzegorz Bancerek
Received July 9, 2007
971. ENTROPY1
Definition and Some Properties of Information Entropy
by Bo Zhang and Yatsuka Nakamura
Received July 9, 2007
972. REWRITE2
String Rewriting Systems
by Micha{\l} Trybulec
Received July 17, 2007
973. MATRIXR2
Determinant and Inverse of Matrices of Real Elements
by Nobuyuki Tamura and Yatsuka Nakamura
Received July 17, 2007
974. RANKNULL
The Rank+Nullity Theorem
by Jesse Alama
Received July 31, 2007
975. LAPLACE
Laplace Expansion
by Karol P\c{a}k and Andrzej Trybulec
Received August 13, 2007
976. MATRIX12
Some Properties of Line and Column Operations on Matrices
by Xiquan Liang, Tao Sun and Dahai Hu
Received August 13, 2007
977. GROUP_10
The Sylow Theorems
by Marco Riccardi
Received August 13, 2007
978. COMPACT1
Alexandroff One Point Compactification
by Czeslaw Bylinski
Received August 13, 2007
979. ARROW
Arrow's Impossibility Theorem
by Freek Wiedijk
Received August 13, 2007
980. BCIALG_2
Congruences and Quotient Algebras of {BCI}-algebras
by Yuzhong Ding and Zhiyong Pang
Received August 28, 2007
981. INT_4
Linear Congruence Relation and Complete Residue Systems
by Xiquan Liang, Li Yan and Junjie Zhao
Received August 28, 2007
982. INTEGRA8
Several Integrability Formulas of Special Functions
by Cuiying Peng, Fuguo Ge and Xiquan Liang
Received August 28, 2007
983. MATRIX13
Basic Properties of the Rank of Matrices over a Field
by Karol P\c{a}k
Received August 28, 2007
984. PCS_0
Basic Operations on Preordered Coherent Spaces
by Klaus E. Grue and Artur Korni{\l}owicz
Received August 28, 2007
985. RINFSUP2
Inferior Limit, Superior Limit and Convergence of Sequences of Extended
Real Numbers
by Hiroshi Yamazaki, Noboru Endou, Yasunari Shidama and Hiroyuki Okazaki
Received August 28, 2007
986. BCIALG_3
Several Classes of {BCK}-algebras and Their Properties
by Tao Sun, Dahai Hu and Xiquan Liang
Received September 19, 2007
987. FDIFF_10
Several Differentiation Formulas of Special Functions -- Part {VI}
by Bo Li and Pan Wang
Received September 19, 2007
988. BSPACE
The Vector Space of Subsets of a Set Based on Symmetric Difference
by Jesse Alama
Received October 9, 2007
989. POLYFORM
Euler's Polyhedron Formula
by Jesse Alama
Received October 9, 2007
990. LOPBAN_5
Uniform Boundedness Principle
by Hideki Sakurai, Hisayoshi Kunimune and Yasunari Shidama
Received October 9, 2007
991. INT_5
Gauss Lemma and Law of Quadratic Reciprocity
by Li Yan, Xiquan Liang and Junjie Zhao
Received October 9, 2007
992. FLANG_3
Regular Expression Quantifiers -- at least $m$ Occurrences
by Micha{\l} Trybulec
Received October 9, 2007
993. COMPL_SP
Complete Spaces
by Karol P\c{a}k
Received October 12, 2007
994. DIFF_2
Difference and Difference Quotient -- Part {II}
by Bo Li, Yanping Zhuang and Xiquan Liang
Received October 25, 2007
995. MESFUNC7
The First Mean Value Theorem for Integrals
by Keiko Narita, Noboru Endou and Yasunari Shidama
Received October 30, 2007
996. MESFUNC8
Egoroff's Theorem
by Noboru Endou, Yasunari Shidama and Keiko Narita
Received October 30, 2007
997. BCIALG_4
BCI-Algebras with Condition (S) and Their Properties
by Tao Sun, Junjie Zhao and Xiquan Liang
Received November 24, 2007
998. GFACIRC2
Stability of n-bit Generalized Full Adder Circuits (GFAs). Part {II}
by Katsumi Wasaki
Received December 18, 2007
999. MATRIX15
Solutions of Linear Equations
by Karol P\c{a}k
Received December 18, 2007
1000. HELLY
Helly property for subtrees
by Jessica Enright and Piotr Rudnicki
Received January 10, 2008
1001. EUCLID_6
Heron's Formula and Ptolemy's Theorem
by Marco Riccardi
Received January 10, 2008
1002. INT_7
Uniqueness of factoring an integer and multiplicative group $Z/pZ^{*}$
by Hiroyuki Okazaki and Yasunari Shidama
Received January 31, 2008
1003. BCIIDEAL
Ideals of BCI-Algebras and Their Properties
by Chenglong Wu and Yuzhong Ding
Received March 3, 2008
1004. C0SP1
Banach Algebra of Bounded Functionals
by Yasunari Shidama, Hikofumi Suzuki and Noboru Endou
Received March 3, 2008
1005. CONVEX4
Convex Sets and Convex Combinations on Complex Linear Spaces
by Hidenori Matsuzaki, Noboru Endou and Yasunari Shidama
Received March 3, 2008
1006. QUATERN2
Inner Products, Group, Ring of Quaternion Numbers
by Fuguo Ge
Received March 18, 2008
1007. HFDIFF_1
Several Higher Differentiation Formulas of Special Functions
by Junjie Zhao, Xiquan Liang and Li Yan
Received March 18, 2008
1008. SIN_COS9
Inverse Trigonometric Functions Arctan and Arccot
by Xiquan Liang and Bing Xie
Received March 18, 2008
1009. SINCOS10
Inverse Trigonometric Functions Arcsec1, Arcsec2, Arccosec1 and Arccosec2
by Bing Xie, Xiquan Liang and Fuguo Ge
Received March 18, 2008
1010. MESFUNC9
The Lebesgue Monotone Convergence Theorem
by Noboru Endou, Keiko Narita and Yasunari Shidama
Received March 18, 2008
1011. AOFA_I00
Mizar Analysis of Algorithms: Algorithms over Integers
by Grzegorz Bancerek
Received March 18, 2008
1012. MATRIX14
Invertibility of Matrices of Field Elements
by Yatsuka Nakamura, Kunio Oniumi and Wenpai Chang
Received April 2, 2008
1013. RAMSEY_1
Ramsey's Theorem
by Marco Riccardi
Received April 18, 2008
1014. ABCMIZ_1
Towards the construction of a model of Mizar concepts
by Grzegorz Bancerek
Received April 21, 2008
1015. MODELC_2
Model Checking, Part II
by Kazuhisa Ishida
Received April 21, 2008
1016. INT_6
Modular Integer Arithmetic
by Christoph Schwarzweller
Received May 13, 2008
1017. BCIALG_5
General Theory of Quasi-Commutative BCI-algebras
by Tao Sun, Weibo Pan, Chenglong Wu and Xiquan Liang
Received May 13, 2008
1018. MATRIXJ1
Block Diagonal Matrices
by Karol P\c{a}k
Received May 13, 2008
1019. MATRLIN2
Linear Map of Matrices
by Karol P\c{a}k
Received May 13, 2008
1020. ROBBINS4
Orthomodular Lattices
by El\.zbieta M\c{a}dra and Adam Grabowski
Received June 27, 2008
1021. AFINSQ_2
Basic Properties and Concept of Selected Subsequence of Zero Based Finite
Sequences
by Yatsuka Nakamura and Hisashi Ito
Received June 27, 2008
1022. VECTSP11
Eigenvalues of a Linear Transformation
by Karol P\c{a}k
Received July 11, 2008
1023. MATRIXJ2
Jordan Matrix Decomposition
by Karol P\c{a}k
Received July 11, 2008
1024. MESFUN10
Fatou's Lemma and the {L}ebesgue's Convergence Theorem
by Noboru Endou, Keiko Narita and Yasunari Shidama
Received July 22, 2008
1025. INTEGR10
Extended {R}iemann Integral of Functions of Real Variable and One-sided
{L}aplace Transform
by Masahiko Yamazaki, Hiroshi Yamazaki, Yasunari Shidama and Yatsuka Nakamura
Received July 22, 2008
1026. MESFUN6C
Integral of Complex-Valued Measurable Function
by Keiko Narita, Noboru Endou and Yasunari Shidama
Received July 30, 2008
1027. MATROID0
Introduction to Matroids
by Grzegorz Bancerek and Yasunari Shidama
Received July 30, 2008
1028. PDIFF_2
Partial Differentiation of Real Binary Functions
by Bing Xie, Xiquan Liang, Hongwei Li and Yanping Zhuang
Received August 5, 2008
1029. MODELC_3
Model Checking, Part {III}
by Kazuhisa Ishida and Yasunari Shidama
Received August 19, 2008
1030. MATRIX16
Basic Properties of Circulant Matrices and Anti-circular Matrices
by Xiaopeng Yue and Xiquan Liang
Received August 26, 2008
1031. LPSPACE1
On $L^1$ Space Formed by Real-valued Partial Functions
by Yasushige Watase, Noboru Endou and Yasunari Shidama
Received August 26, 2008
1032. BCIALG_6
{BCI}-Homomorphisms
by Yuzhong Ding, Fuguo Ge and Chenglong Wu
Received August 26, 2008
1033. FTACELL1
Stability of the 4-2 Binary Addition Circuit Cells. Part {I}
by Katsumi Wasaki
Received August 28, 2008
1034. FDIFF_11
Several Differentiation Formulas of Special Functions -- Part {VII}
by Fuguo Ge and Bing Xie
Received September 23, 2008
1035. LOPBAN_6
Open Mapping Theorem
by Hideki Sakurai, Hisayoshi Kunimune and Yasunari Shidama
Received September 23, 2008
1036. EUCLID_7
The Real Vector Spaces of Finite Sequences Are Finite Dimensional
by Yatsuka Nakamura, Artur Korni{\l}owicz, Nagato Oya
and Yasunari Shidama
Received September 23, 2008
1037. INTEGRA9
Several Integrability Formulas of Some Functions, Orthogonal Polynomials
and Norm Functions
by Bo Li, Yanping Zhuang, Bing Xie and Pan Wang
Received October 14, 2008
1038. INTEGR11
Several Integrability Formulas of Special Functions -- Part {II}
by Bo Li, Yanping Zhuang, Yanhong Men and Xiquan Liang
Received October 14, 2008
1039. QUATERN3
Some Operations on Quaternion Numbers
by Bo Li, Pan Wang, Xiquan Liang and Yanping Zhuang
Received October 14, 2008
1040. PETRI_2
Cell Petri Net Concepts
by Mitsuru Jitsukawa, Pauline N. Kawamoto, Yasunari Shidama and Yatsuka Nakamura
Received October 14, 2008
1041. VALUED_2
Arithmetic Operations on Functions from Sets into Functional Sets
by Artur Korni{\l}owicz
Received October 15, 2008
1042. CFDIFF_1
Complex Function Differentiability
by Chanapat Pacharapokin, Hiroshi Yamazaki, Yasunari Shidama and Yatsuka Nakamura
Received November 4, 2008
1043. KOLMOG01
Kolmogorov's Zero-one Law
by Agnes Doll
Received November 4, 2008
1044. PDIFF_3
Second-order Partial Differentiation of Real Binary Functions
by Bing Xie, Xiquan Liang and Xiuzhuan Shen
Received December 16, 2008
1045. MESFUN7C
The Measurability of Complex-Valued Functional Sequences
by Keiko Narita, Noboru Endou and Yasunari Shidama
Received December 16, 2008
1046. MEMBER_1
Collective Operations on Number-Membered Sets
by Artur Korni{\l}owicz
Received December 19, 2008
1047. POLYEQ_5
Solution of Cubic and Quartic Equations
by Marco Riccardi
Received March 3, 2009
1048. NAT_5
The Perfect Number Theorem and Wilson's Theorem
by Marco Riccardi
Received March 3, 2009
1049. RANDOM_1
Probability on Finite Set and Real Valued Random Variables
by Hiroyuki Okazaki and Yasunari Shidama
Received March 17, 2009
1050. MESFUN9C
Lebesgue's Convergence Theorem of Complex-Valued Function
by Keiko Narita, Noboru Endou and Yasunari Shidama
Received March 17, 2009
1051. METRIZTS
Basic Properties of Metrizable Topological Spaces
by Karol P\c{a}k
Received March 31, 2009
1052. GR_CY_3
Properties of Primes and Multiplicative Group of a Field
by Kenichi Arai and Hiroyuki Okazaki
Received April 7, 2009
1053. CFDIFF_2
Cauchy-Riemann Differential Equations of Complex Functions
by Hiroshi Yamazaki, Yasunari Shidama, Chanapat Pacharapokin and Yatsuka Nakamura
Received April 7, 2009
1054. MEASURE8
The Hopf Extension Theorem of Measure
by Noboru Endou, Hiroyuki Okazaki and Yasunari Shidama
Received April 7, 2009
1055. REWRITE3
Labelled State Transition Systems
by Micha{\l} Trybulec
Received May 5, 2009
1056. DIST_1
Probability on Finite and Discrete Set and Uniform Distribution
by Hiroyuki Okazaki
Received May 5, 2009
1057. INTEGR15
Riemann Integral of Functions $\mathbbbR$ into $\mathbbbR^n$
by Keiichi Miyajima and Yasunari Shidama
Received May 5, 2009
1058. FUNCT_8
Basic properties of even and odd functions
by Bo Li and Yanhong Men
Received May 25, 2009
1059. FSM_3
Equivalence of Epsilon, Nondeterministic [Finite] Automata and Deterministic
[Finite] Automata
by Micha{\l} Trybulec
Received May 25, 2009
1060. TOPDIM_1
Small {I}nductive {D}imension of {T}opological {S}paces
by Karol P\c{a}k
Received June 29, 2009
1061. GROUP_11
On Rough Subgroup of a Group
by Xiquan Liang and Dailu Li
Received August 7, 2009
1062. TOPDIM_2
Small Inductive Dimension of Topological Spaces, Part {II}
by Karol P\c{a}k
Received August 7, 2009
1063. DILWORTH
Dilworth's Decomposition Theorem for Posets
by Piotr Rudnicki
Received September 17, 2009
1064. INTEGR1C
Complex Integral
by Masahiko Yamazaki, Hiroshi Yamazaki, Katsumi Wasaki and Yasunari Shidama
Received October 10, 2009
1065. INTERVA1
On the Lattice of Intervals and Rough Sets
by Adam Grabowski and Magdalena Jastrz\c{e}bska
Received October 10, 2009
1066. FUNCT_9
Basic Properties of Periodic Functions
by Bo Li, Yanhong Men, Dailu Li and Xiquan Liang
Received October 10, 2009
1067. EUCLID_8
Vector Function and its Differentiation Formulas in 3-dimensional Euclidean
Spaces
by Xiquan Liang, Piqing Zhao and Ou Bai
Received October 10, 2009
1068. ORDINAL5
Epsilon Numbers and Cantor Normal Form
by Grzegorz Bancerek
Received October 20, 2009
1069. C0SP2
Banach Algebra of Continuous Functionals
by Kanazashi Katuhiko, Noboru Endou and Yasunari Shidama
Received October 20, 2009
1070. ALGSTR_4
Free Magmas
by Marco Riccardi
Received October 20, 2009
1071. INTEGR12
Integrability Formulas -- Part {I}
by Bo Li and Na Ma
Received November 7, 2009
1072. PDIFF_4
Partial Differentiation of Real Ternary Functions
by Takao Inou\'e, Bing Xie and Xiquan Liang
Received November 7, 2009
1073. POSET_1
Fix-point Theorem for Continuous Functions on Chain-complete Posets
by Kazuhisa Ishida and Yasunari Shidama
Received November 10, 2009
1074. GRNILP_1
Nilpotent Groups
by Dailu Li, Xiquan Liang and Yanhong Men
Received November 10, 2009
1075. DIFF_3
Difference and Difference Quotient -- Part {III}
by Xiquan Liang and Ling Tang
Received November 17, 2009
1076. ABCMIZ_A
A Model of Mizar Concepts -- Unification
by Grzegorz Bancerek
Received November 20, 2009
1077. FIB_NUM4
Representation of the {F}ibonacci and {L}ucas Numbers in Terms of
the Floor and Ceiling Functor
by Magdalena Jastrz\c{e}bska
Received November 30, 2009
1078. EUCLID_9
The Correspondence Between $n$-dimensional {E}uclidean Space and the
Product of $n$ Real Lines
by Artur Korni{\l}owicz
Received November 30, 2009
1079. RLAFFIN1
Affine Independence in Vector Spaces
by Karol P\c{a}k
Received December 18, 2009
1080. SIMPLEX0
Abstract Simplicial Complexes
by Karol P\c{a}k
Received December 18, 2009
1081. RVSUM_2
The Sum and Product of Finite Sequences of Complex Numbers
by Keiichi Miyajima and Takahiro Kato
Received January 12, 2010
1082. PDIFF_5
Second-order Partial Differentiation of Real Ternary Functions
by Takao Inou\'e
Received January 26, 2010
1083. INTEGR13
Integrability Formulas -- Part {II}
by Bo Li, Na Ma and Xiquan Liang
Received February 4, 2010
1084. INTEGR14
Integrability Formulas -- Part {III}
by Bo Li and Na Ma
Received February 4, 2010
1085. LPSPACE2
On $L^p$ Space Formed by Real-valued Partial Functions
by Yasushige Watase, Noboru Endou and Yasunari Shidama
Received February 4, 2010
1086. TOPS_4
Miscellaneous Facts about Open Functions and Continuous Functions
by Artur Korni{\l}owicz
Received February 9, 2010
1087. TOPREALC
On the Continuity of Some Functions
by Artur Korni{\l}owicz
Received February 9, 2010
1088. RLAFFIN2
The Geometric Interior in Real Linear Spaces
by Karol P\c{a}k
Received February 9, 2010
1089. SIMPLEX1
Sperner's Lemma
by Karol P\c{a}k
Received February 9, 2010
1090. CARDFIN2
Counting Derangements, Counting Non Bijective Functions and the Birthday
Problem
by Cezary Kaliszyk
Received February 23, 2010
1091. INTEGR16
Riemann Integral of Functions $\mathbbbR$ into $\mathbbbC$
by Keiichi Miyajima, Takahiro Kato and Yasunari Shidama
Received February 23, 2010
1092. PDIFF_6
Differentiation of Vector-Valued Functions on $n$-Dimensional Real Normed
Linear Spaces
by Takao Inou\'e, Noboru Endou and Yasunari Shidama
Received February 23, 2010
1093. RANDOM_2
Probability Measure on Discrete Spaces and Algebra of Real Valued Random
Variables
by Hiroyuki Okazaki and Yasunari Shidama
Received March 16, 2010
1094. PDIFF_7
Partial Differentiation of Vector-Valued Functions on $n$-Dimensional Real
Normed Linear Spaces
by Takao Inou\'e, Adam Naumowicz, Noboru Endou and Yasunari Shidama
Received April 22, 2010
1095. GROUPP_1
Some Properties of $p$-Groups and Commutative $p$-Groups
by Xiquan Liang and Dailu Li
Received April 29, 2010
1096. INTEGR18
Riemann Integral of Functions from $\mathbbbR$ into Real Normed Space
by Keiichi Miyajima, Takahiro Kato and Yasunari Shidama
Received May 20, 2010
1097. GROUP_12
Normal Subgroup of Product of Groups
by Hiroyuki Okazaki, Kenichi Arai and Yasunari Shidama
Received July 2, 2010
1098. MYCIELSK
The {M}ycielskian of a Graph
by Piotr Rudnicki and Lorna Stewart
Received July 2, 2010
1099. DIFF_4
Difference and Difference Quotient -- Part {IV}
by Xiquan Liang, Ling Tang and Xichun Jiang
Received July 12, 2010
1100. MFOLD_1
The Definition of Topological Manifolds
by Marco Riccardi
Received August 17, 2010
1101. NFCONT_3
More on Continuous Functions on Normed Linear Spaces
by Hiroyuki Okazaki, Noboru Endou and Yasunari Shidama
Received August 17, 2010
1102. PRVECT_3
Cartesian Products of Family of Real Linear Spaces
by Hiroyuki Okazaki, Noboru Endou and Yasunari Shidama
Received August 17, 2010
1103. RLVECT_X
Formalization of Integral Linear Space
by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
Received August 17, 2010
1104. PDIFF_8
Partial Differentiation, Differentiation and Continuity on $n$-Dimensional
Real Normed Linear Spaces
by Takao Inou\'e, Adam Naumowicz, Noboru Endou and Yasunari Shidama
Received October 13, 2010
1105. NDIFF_3
Differentiable Functions into Real Normed Spaces
by Hiroyuki Okazaki, Noboru Endou, Keiko Narita and Yasunari Shidama
Received October 13, 2010
1106. CGAMES_1
Conway's Games and Some of Their Basic Properties
by Robin Nittka
Received October 13, 2010
1107. ORDINAL6
Veblen Hierarchy
by Grzegorz Bancerek
Received October 18, 2010
1108. EXCHSORT
Sorting by Exchanging
by Grzegorz Bancerek
Received October 18, 2010
1109. MATRTOP1
Linear Transformations of Euclidean Topological Spaces
by Karol P\kak
Received October 26, 2010
1110. MATRTOP2
Linear Transformations of Euclidean Topological Spaces. Part {II}
by Karol P\kak
Received October 26, 2010
1111. LTLAXIO1
The Axiomatization of Propositional Linear Time Temporal Logic
by Mariusz Giero
Received November 20, 2010
1112. CC0SP1
Banach Algebra of Bounded Complex-Valued Functionals
by Katuhiko Kanazashi, Hiroyuki Okazaki and Yasunari Shidama
Received November 20, 2010
1113. MAZURULM
Mazur-Ulam Theorem
by Artur Korni{\l}owicz
Received December 21, 2010
1114. EC_PF_1
Set of Points on Elliptic Curve in Projective Coordinates
by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
Received December 21, 2010
1115. RLAFFIN3
Continuity of Barycentric Coordinates in Euclidean Topological Spaces
by Karol P\kak
Received December 21, 2010
1116. SIMPLEX2
Brouwer Fixed Point Theorem for Simplexes
by Karol P\kak
Received December 21, 2010
1117. BROUWER2
Brouwer Fixed Point Theorem in the General Case
by Karol P\kak
Received December 21, 2010
1118. FOMODEL0
Preliminaries to Classical First-order Model Theory
by Marco B. Caminati
Received December 29, 2010
1119. FOMODEL1
Definition of first order language with arbitrary alphabet. Syntax of
terms, atomic formulas and their subterms.
by Marco B. Caminati
Received December 29, 2010
1120. FOMODEL2
First order languages: syntax, part two; semantics.
by Marco B. Caminati
Received December 29, 2010
1121. FOMODEL3
Free interpretation, quotient interpretation and substitution of a letter
with a term for first order languages.
by Marco B. Caminati
Received December 29, 2010
1122. FOMODEL4
Sequent calculus, derivability, provability. Goedel's completeness theorem.
by Marco B. Caminati
Received December 29, 2010
1123. CAYLEY
Cayley's Theorem
by Artur Korni{\l}owicz
Received December 29, 2010
1124. BOR_CANT
Borel-Cantelli Lemma
by Peter Jaeger
Received January 31, 2011
1125. NFCONT_4
More on the Continuity of Real Functions
by Keiko Narita, Artur Korni{\l}owicz and Yasunari Shidama
Received February 22, 2011
1126. STACKS_1
Representation Theorem for Stacks
by Grzegorz Bancerek
Received February 22, 2011
1127. FINANCE1
Elementary Introduction to Stochastic Finance in Discrete Time
by Peter Jaeger
Received March 22, 2011
1128. FVALUAT1
Valuation Theory, Part {I}
by Grzegorz Bancerek, Hidetsune Kobayashi and Artur Korni{\l}owicz
Received April 7, 2011
1129. CC0SP2
Banach Algebra of Complex-Valued Continuous Functionals and Space of
Complex-valued Continuous Functionals with Bounded Support
by Katuhiko Kanazashi, Hiroyuki Okazaki and Yasunari Shidama
Received May 30, 2011
1130. MATRTOP3
The Rotation Group
by Karol P\kak
Received May 30, 2011
1131. NDIFF_5
Differentiable Functions on Normed Linear Spaces
by Yasunari Shidama
Received June 2, 2011
1132. MFOLD_2
Planes and Spheres as Topological Manifolds. Stereographic Projection
by Marco Riccardi
Received June 6, 2011
1133. ZMODUL01
$\mathbb Z$-modules
by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
Received September 5, 2011
1134. MORPH_01
Morphology for Image Processing, Part {I}
by Hiroshi Yamazaki, Czes\l aw Byli\'nski and Katsumi Wasaki
Received September 21, 2011
1135. NDIFF_4
The Differentiable Functions from $\mathbbR$ into ${\mathbbR}^n$
by Keiko Narita, Artur Korni\l owicz and Yasunari Shidama
Received September 28, 2011
1136. MATRIX17
Some Basic Properties of Some Special Matrices, Part {III}
by Xiquan Liang and Tao Wang
Received October 23, 2011
1137. INTEGR19
Riemann Integral of Functions from $\mathbbbR$ into $n$-dimensional Real
Normed Space
by Keiichi Miyajima, Artur Korni{\l}owicz and Yasunari Shidama
Received October 27, 2011
1138. EC_PF_2
Operations of Points on Elliptic Curve in Projective Coordinates
by Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima and Yasunari Shidama
Received November 3, 2011
1139. TOPALG_6
Fundamental Group of $n$-sphere for $n \geq 2$
by Marco Riccardi and Artur Korni{\l}owicz
Received November 3, 2011
1140. BORSUK_7
The {B}orsuk-Ulam Theorem
by Artur Korni{\l}owicz and Marco Riccardi
Received November 3, 2011
1141. PDIFF_9
Higher Order Partial Differentiation
by Noboru Endou, Hiroyuki Okazaki and Yasunari Shidama
Received November 20, 2011
1142. DESCIP_1
Formalization of the Data Encryption Standard
by Hiroyuki Okazaki and Yasunari Shidama
Received November 30, 2011
1143. MMLQUERY
Semantic of MML Query
by Grzegorz Bancerek
Received December 18, 2011
1144. MENELAUS
Routh's, {M}enelaus' and Generalized {C}eva's Theorems
by Boris A. Shminke
Received January 16, 2012
1145. SCMYCIEL
Simple Graphs as Simplicial Complexes: the {M}ycielskian of a Graph
by Piotr Rudnicki and Lorna Stewart
Received February 8, 2012
1146. NTALGO_1
Extended Euclidean Algorithm and CRT Algorithm
by Hiroyuki Okazaki, Yosiki Aoki and Yasunari Shidama
Received February 8, 2012
1147. RATFUNC1
Introduction to Rational Functions
by Christoph Schwarzweller
Received February 8, 2012
1148. QC_TRANS
Transition of Consistency and Satisfiability under Language Extensions
by Julian J. Schl\"oder and Peter Koepke
Received May 7, 2012
1149. GOEDCPUC
The G\"odel Completeness Theorem for Uncountable Languages
by Julian J. Schl\"oder and Peter Koepke
Received May 7, 2012
1150. ZMODUL02
Quotient Module of $\mathbb Z$-module
by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
Received May 7, 2012
1151. LTLAXIO2
The Derivations of Temporal Logic Formulas
by Mariusz Giero
Received May 7, 2012
1152. LTLAXIO3
The Properties of Sets of Temporal Logic Subformulas
by Mariusz Giero
Received May 7, 2012
1153. LTLAXIO4
Weak Completeness Theorem for Propositional Linear Time Temporal Logic
by Mariusz Giero
Received May 7, 2012
1154. FRIENDS1
The Friendship Theorem
by Karol P\kak
Received May 15, 2012
1155. MSAFREE4
Free Term Algebras
by Grzegorz Bancerek
Received May 15, 2012
1156. DIST_2
Posterior Probability on Finite Set
by Hiroyuki Okazaki
Received July 4, 2012
1157. INT_8
Basic Properties of Primitive Root and Order Function
by Na Ma and Xiquan Liang
Received August 6, 2012
1158. LOPBAN_7
Banach's Continuous Inverse Theorem and Closed Graph Theorem
by Hideki Sakurai, Hiroyuki Okazaki and Yasunari Shidama
Received August 6, 2012
1159. ZMODUL03
Free $\mathbb Z$-module
by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
Received August 6, 2012
1160. CAYLDICK
Cayley-Dickson Construction
by Artur Korni{\l}owicz
Received August 6, 2012
1161. ORDEQ_01
Contracting Mapping on Normed Linear Space
by Keiichi Miyajima, Artur Korni{\l}owicz and Yasunari Shidama
Received August 19, 2012
1162. ALTCAT_5
Products in Categories without Uniqueness of { \bf cod } and { \bf dom }
by Artur Korni{\l}owicz
Received August 19, 2012
1163. AOFA_A00
Program Algebra over an Algebra
by Grzegorz Bancerek
Received August 27, 2012
1164. GROUP_14
Isomorphisms of Direct Products of Finite Cyclic Groups
by Kenichi Arai, Hiroyuki Okazaki and Yasunari Shidama
Received August 27, 2012
1165. LPSPACC1
On $L^1$ Space Formed by Complex-valued Partial Functions
by Yasushige Watase, Noboru Endou and Yasunari Shidama
Received August 27, 2012
1166. AOFA_A01
Analysis of Algorithms: An Example of a Sort Algorithm
by Grzegorz Bancerek
Received November 9, 2012
1167. CKSPACE1
The $C^k$ Space
by Katuhiko Kanazashi, Hiroyuki Okazaki and Yasunari Shidama
Received November 9, 2012
1168. RANDOM_3
Random Variables and Product of Probability Spaces
by Hiroyuki Okazaki and Yasunari Shidama
Received December 1, 2012
1169. MMLQUER2
The Semantics of MML Query -- Ordering
by Grzegorz Bancerek
Received December 1, 2012
1170. HURWITZ2
A Test for the Stability of Networks
by Agnieszka Rowi\'nska-Schwarzweller and Christoph Schwarzweller
Received January 17, 2013
1171. ROUGHS_2
Relational Formal Characterization of Rough Sets
by Adam Grabowski
Received January 17, 2013
1172. GROUP_17
Isomorphisms of Direct Products of Finite Commutative Groups
by Hiroyuki Okazaki, Hiroshi Yamazaki and Yasunari Shidama
Received January 31, 2013
1173. NBVECTSP
$n$-dimensional Binary Vector Spaces
by Kenichi Arai and Hiroyuki Okazaki
Received April 17, 2013
1174. TOPGEN_6
Some Properties of the {S}orgenfrey Line and the {S}orgenfrey Plane
by Adam J.J. St. Arnaud and Piotr Rudnicki
Received April 17, 2013
1175. NUMERAL2
More on Divisibility Criteria for Selected Primes
by Adam Naumowicz and Rados{\l}aw Piliszek
Received May 19, 2013
1176. NDIFF_6
Differentiation in Normed Spaces
by Noboru Endou and Yasunari Shidama
Received May 19, 2013
1177. NUMPOLY1
Polygonal Numbers
by Adam Grabowski
Received May 19, 2013
1178. GAUSSINT
Gaussian Integers
by Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima and Yasunari Shidama
Received May 19, 2013
1179. TOPALG_7
Commutativeness of Fundamental Groups of Topological Groups
by Artur Korni{\l}owicz
Received May 19, 2013
1180. HUFFMAN1
Constructing Binary {H}uffman Tree
by Hiroyuki Okazaki, Yuichi Futa and Yasunari Shidama
Received June 18, 2013
1181. INTEGR20
Riemann Integral of Functions from $\mathbbbR$ into Real {B}anach Space
by Keiko Narita, Noboru Endou and Yasunari Shidama
Received June 18, 2013
1182. MOEBIUS2
On Square-free Numbers
by Adam Grabowski
Received July 12, 2013
1183. DBLSEQ_1
Double Sequences and Limits
by Noboru Endou, Hiroyuki Okazaki and Yasunari Shidama
Received August 31, 2013
1184. AESCIP_1
Formalization of the Advanced Encryption Standard -- Part {I}
by Kenichi Arai and Hiroyuki Okazaki
Received October 7, 2013
1185. INTEGR21
The Linearity of Riemann Integral on Functions from $\mathbbbR$ into Real
{B}anach Space
by Keiko Narita, Noboru Endou and Yasunari Shidama
Received October 7, 2013
1186. CAT_6
Object-Free Definition of Categories
by Marco Riccardi
Received October 7, 2013
1187. GROUP_18
Isomorphisms of Direct Products of Cyclic Groups of Prime-power Order
by Hiroshi Yamazaki, Hiroyuki Okazaki, Kazuhisa Nakasho and Yasunari Shidama
Received October 7, 2013
1188. LATTICEA
Prime Filters and Ideals in Distributive Lattices
by Adam Grabowski
Received October 7, 2013
1189. PREFER_1
Introduction to Formal Preference Spaces
by Eliza Niewiadomska and Adam Grabowski
Received October 7, 2013
1190. ALTCAT_6
Coproducts in Categories without Uniqueness of { \bf cod } and { \bf
dom}
by Maciej Goli\'nski and Artur Korni{\l}owicz
Received December 8, 2013
1191. PETRI_3
Formulation of Cell Petri Nets
by Mitsuru Jitsukawa, Pauline N. Kawamoto and Yasunari Shidama
Received December 8, 2013
1192. NDIFF_7
Isometric Differentiable Functions on Real Normed Space
by Yuichi Futa, Noboru Endou and Yasunari Shidama
Received December 31, 2013
1193. ORDEQ_02
Differential Equations on Functions from $\mathbbR$ into Real {B}anach
Space
by Keiko Narita, Noboru Endou and Yasunari Shidama
Received December 31, 2013
1194. ZMODUL04
Submodule of free $\mathbb Z$-module
by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
Received December 31, 2013
1195. POSET_2
Definition of Flat Poset and Existence Theorems for Recursive Call
by Kazuhisa Ishida, Yasunari Shidama and Adam Grabowski
Received February 11, 2014
1196. TIETZE_2
Tietze Extension Theorem for $n$-dimensional Spaces
by Karol P\kak
Received February 11, 2014
1197. BROUWER3
Brouwer Invariance of Domain Theorem
by Karol P\kak
Received February 11, 2014
1198. PETRI_DF
The Formalization of Decision Free {P}etri Net
by Pratima K. Shah, Pauline N. Kawamoto and Mariusz Giero
Received March 31, 2014
1199. ABSRED_0
Abstract Reduction Systems and Idea of {K}nuth {B}endix Completion
Algorithm
by Grzegorz Bancerek
Received March 31, 2014
1200. DBLSEQ_2
Double Series and Sums
by Noboru Endou
Received March 31, 2014
1201. DUALSP01
Dual Spaces and Hahn-Banach's Theorem
by Keiko Narita, Noboru Endou and Yasunari Shidama
Received March 31, 2014
1202. SRINGS_1
Semiring of Sets
by Roland Coghetto
Received March 31, 2014
1203. SRINGS_2
Semiring of Sets: Examples
by Roland Coghetto
Received March 31, 2014
1204. ROUGHS_4
Topological Interpretation of Rough Sets
by Adam Grabowski
Received March 31, 2014
1205. HILBERT4
Pseudo-canonical Formulae are Classical
by Marco B. Caminati and Artur Korni{\l}owicz
Received May 25, 2014
1206. LAGRA4SQ
Lagrange's Four-Square Theorem
by Yasushige Watase
Received June 4, 2014
1207. NAT_6
Proth Numbers
by Christoph Schwarzweller
Received June 4, 2014
1208. BALLOT_1
Bertrand's Ballot Theorem
by Karol P\kak
Received June 13, 2014
1209. MSAFREE5
Term Context
by Grzegorz Bancerek
Received June 13, 2014
1210. RVSUM_3
Cauchy Mean Theorem
by Adam Grabowski
Received June 13, 2014
1211. GTARSKI1
Tarski Geometry Axioms
by William Richter, Adam Grabowski and Jesse Alama
Received June 16, 2014
1212. GRAPH_3A
A Note on the Seven Bridges of K\"onigsberg Problem
by Adam Naumowicz
Received June 16, 2014
1213. MFOLD_0
Topological Manifolds
by Karol P\kak
Received June 16, 2014
1214. ZMODUL05
Rank of Submodule, Linear Transformations and Linearly Independent Subsets
of $\mathbb Z$-module
by Kazuhisa Nakasho, Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
Received July 10, 2014
1215. FINANCE2
Events of Borel Sets, Construction of Borel Sets and Random Variables
for Stochastic Finance
by Peter Jaeger
Received July 10, 2014
1216. NEWTON01
Some Remarkable Identities Involving Numbers
by Rafa{\l} Ziobro
Received September 5, 2014
1217. NORMSP_3
Topological Properties of Real Normed Space
by Kazuhisa Nakasho, Yuichi Futa and Yasunari Shidama
Received September 15, 2014
1218. AOFA_L00
Algebraic Approach to Algorithmic Logic
by Grzegorz Bancerek
Received September 15, 2014
1219. LATTAD_1
Formalization of Generalized Almost Distributive Lattices
by Adam Grabowski
Received September 26, 2014
1220. VSDIFF_1
Difference of Function on Vector Space over $\mathbbF$
by Kenichi Arai, Ken Wakabayashi and Hiroyuki Okazaki
Received September 26, 2014
1221. ZMODUL06
Torsion $\mathbb Z$-module and Torsion-free $\mathbb Z$-module
by Yuichi Futa, Hiroyuki Okazaki, Kazuhisa Nakasho and Yasunari Shidama
Received November 29, 2014
1222. RING_2
The First Isomorphism Theorem and Other Properties of Rings
by Artur Korni{\l}owicz and Christoph Schwarzweller
Received November 29, 2014
1223. DUALSP02
Bidual Spaces and Reflexivity of Real Normed Spaces
by Keiko Narita, Noboru Endou and Yasunari Shidama
Received November 29, 2014
1224. EUCLID10
Some Facts about Trigonometry and Euclidean Geometry
by Roland Coghetto
Received November 29, 2014
1225. FUZNUM_1
The Formal Construction of Fuzzy Numbers
by Adam Grabowski
Received December 31, 2014
1226. CAT_7
Categorical Pullbacks
by Marco Riccardi
Received December 31, 2014
1227. GROUP_19
Definition and Properties of Direct Sum Decomposition of Groups
by Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki and Yasunari Shidama
Received December 31, 2014
1228. ZMATRLIN
Matrix of $\mathbb Z$-module
by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
Received February 18, 2015
1229. SRINGS_3
$\sigma$-ring and $\sigma$-algebra of Sets
by Noboru Endou, Kazuhisa Nakasho and Yasunari Shidama
Received February 18, 2015
1230. NORMSP_4
Separability of Real Normed Spaces and Its Basic Properties
by Kazuhisa Nakasho and Noboru Endou
Received February 26, 2015
1231. GROUP_20
Equivalent Expressions of Direct Sum Decomposition of Groups
by Kazuhisa Nakasho, Hiroyuki Okazaki, Hiroshi Yamazaki and Yasunari Shidama
Received February 26, 2015
1232. EUCLID11
Morley's Trisector Theorem
by Roland Coghetto
Received March 26, 2015
1233. FLEXARY1
Flexary Operations
by Karol P\kak
Received March 26, 2015
1234. EULRPART
{E}uler's {P}artition {T}heorem
by Karol P\kak
Received March 26, 2015
1235. DIOPHAN1
Introduction to {D}iophantine Approximation
by Yasushige Watase
Received April 19, 2015
1236. SRINGS_4
Finite Product of Semiring of Sets
by Roland Coghetto
Received April 19, 2015
1237. NELSON_1
Two Axiomatizations of {N}elson Algebras
by Adam Grabowski
Received April 19, 2015
1238. GROUP_1A
Groups -- Additive Notation
by Roland Coghetto
Received April 30, 2015
1239. POLNOT_1
Polish Notation
by Taneli Huuskonen
Received April 30, 2015
1240. GRZLOG_1
Grzegorczyk's Logics, Part 1
by Taneli Huuskonen
Received April 30, 2015
1241. CARDFIL2
Convergent Filter Bases
by Roland Coghetto
Received June 30, 2015
1242. ASYMPT_2
Polynomially Bounded Sequences and Polynomial Sequences
by Hiroyuki Okazaki and Yuichi Futa
Received June 30, 2015
1243. NEWTON02
Fermat's Little Theorem via Divisibility of {N}ewton's Binomial
by Rafa{\l} Ziobro
Received June 30, 2015
1244. DUALSP03
Weak Convergence and Weak* Convergence
by Keiko Narita, Noboru Endou and Yasunari Shidama
Received July 1, 2015
1245. DUALSP04
The Orthogonal Projection and {R}iesz Representation Theorem
by Keiko Narita, Noboru Endou and Yasunari Shidama
Received July 1, 2015
1246. DBLSEQ_3
Extended Real Valued Double Sequence and Its Convergence
by Noboru Endou
Received July 1, 2015
1247. CARDFIL3
Summable Family in a Commutative Group
by Roland Coghetto
Received August 14, 2015
1248. FINTOPO7
Topology from Neighbourhoods
by Roland Coghetto
Received August 14, 2015
1249. ZMODUL07
Torsion-part of $\mathbb Z$-module
by Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama
Received August 14, 2015
1250. MEASURE9
Construction of Measure from Semialgebra of Sets
by Noboru Endou
Received August 14, 2015
1251. PETERSON
Event-based Proof of the Mutual Exclusion Property of {P}eterson's
Algorithm
by Ievgen Ivanov, Mykola Nikitchenko and Uri Abraham
Received August 14, 2015
1252. RING_3
Characteristic of Rings; Prime Fields
by Christoph Schwarzweller and Artur Korni{\l}owicz
Received August 14, 2015
1253. CAT_8
Exponential Objects
by Marco Riccardi
Received August 15, 2015
1254. ASYMPT_3
Algebra of Polynomially Bounded Sequences and Negligible Functions
by Hiroyuki Okazaki
Received August 15, 2015
1255. LTLAXIO5
Propositional Linear Time Temporal Logic with Initial Semantics
by Mariusz Giero
Received October 22, 2015
1256. LATSTONE
Stone Lattices
by Adam Grabowski
Received October 22, 2015
1257. FINANCE3
Modelling Real World Using Stochastic Processes and Filtration
by Peter Jaeger
Received December 30, 2015
1258. EUCLID12
Circumcenter, Circumcircle, and Centroid of a Triangle
by Roland Coghetto
Received December 30, 2015
1259. EUCLID13
Altitude, Orthocenter of a Triangle and Triangulation
by Roland Coghetto
Received December 30, 2015
1260. ZMODUL08
Divisible $\mathbb Z$-modules
by Yuichi Futa and Yasunari Shidama
Received December 30, 2015
1261. ZMODLAT1
Lattice of $\mathbb Z$-module
by Yuichi Futa and Yasunari Shidama
Received December 30, 2015
1262. MEASUR10
Product Pre-Measure
by Noboru Endou
Received December 31, 2015
1263. GROUP_21
Conservation Rules of Direct Sum Decomposition of Groups
by Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki and Yasunari Shidama
Received December 31, 2015
1264. BAGORD_2
On Multiset Ordering
by Grzegorz Bancerek
Received December 31, 2015
1265. COUSIN
Cousin's Lemma
by Roland Coghetto
Received December 31, 2015
1266. SRINGS_5
Chebyshev Distance
by Roland Coghetto
Received December 31, 2015
1267. ROUGHS_3
Binary Relations-Based Rough Sets -- An Automated Approach
by Adam Grabowski
Received February 15, 2016
1268. GTARSKI2
Tarski Geometry Axioms -- Part {II}
by Roland Coghetto and Adam Grabowski
Received June 30, 2016
1269. TOPMETR4
Compactness in Metric Spaces
by Kazuhisa Nakasho, Keiko Narita and Yasunari Shidama
Received June 30, 2016
1270. CARDFIL4
Double Sequences and Iterated Limits in Regular Space
by Roland Coghetto
Received June 30, 2016
1271. NEWTON03
Prime Factorization of Sums and Differences of Two Like Powers
by Rafa{\l} Ziobro
Received June 30, 2016
1272. INTEGR22
Riemann-Stieltjes Integral
by Keiko Narita, Kazuhisa Nakasho and Yasunari Shidama
Received June 30, 2016
1273. UNIFORM2
Quasi-uniform Space
by Roland Coghetto
Received June 30, 2016
1274. UNIFORM3
Uniform Space
by Roland Coghetto
Received June 30, 2016
1275. RING_4
Some Algebraic Properties of Polynomial Rings
by Christoph Schwarzweller, Artur Korni{\l}owicz and Agnieszka Rowinska-Schwarzweller
Received June 30, 2016
1276. ANPROJ_8
Homography in $\mathbbRP^2$
by Roland Coghetto
Received October 18, 2016
1277. INTEGR23
The Basic Existence Theorem of Riemann-Stieltjes Integral
by Kazuhisa Nakasho, Keiko Narita and Yasunari Shidama
Received October 18, 2016
1278. NEWTON04
On Subnomials
by Rafa{\l} Ziobro
Received October 18, 2016
1279. LEIBNIZ1
Leibniz's Series for Pi
by Karol P\kak
Received October 18, 2016
1280. PL_AXIOM
The Axiomatization of Propositional Logic
by Mariusz Giero
Received October 18, 2016
1281. ALGNUM_1
Algebraic Numbers
by Yasushige Watase
Received December 15, 2016
1282. NIVEN
Niven's Theorem
by Artur Korni{\l}owicz and Adam Naumowicz
Received December 15, 2016
1283. MEASUR11
Fubini's Theorem on Measure
by Noboru Endou
Received February 23, 2017
1284. POLYDIFF
Differentiability of Polynomials over Reals
by Artur Korni{\l}owicz
Received February 23, 2017
1285. LIOUVIL1
Introduction to {L}iouville Numbers
by Adam Grabowski and Artur Korni{\l}owicz
Received February 23, 2017
1286. LIOUVIL2
All Liouville Numbers are Transcendental
by Artur Korni{\l}owicz, Adam Naumowicz and Adam Grabowski
Received February 23, 2017
1287. ANPROJ_9
Group of Homography in Real Projective Plane
by Roland Coghetto
Received March 17, 2017
1288. REALALG1
Ordered Rings and Fields
by Christoph Schwarzweller
Received March 17, 2017
1289. ZMODLAT2
Embedded Lattice and Properties of {G}ram Matrix
by Yuichi Futa and Yasunari Shidama
Received March 17, 2017
1290. POLYVIE1
Vieta's Formula about the Sum of Roots of Polynomials
by Artur Korni{\l}owicz and Karol P\kak
Received May 25, 2017
1291. FUZNORM1
Basic Formal Properties of Triangular Norms and Conorms
by Adam Grabowski
Received June 27, 2017
1292. FINANCE4
Introduction to Stopping Time in Stochastic Finance Theory
by Peter Jaeger
Received June 27, 2017
1293. PASCAL
Pascal's Theorem in Real Projective Plane
by Roland Coghetto
Received June 27, 2017
1294. ORDERS_5
About Quotient Orders and Ordering Sequences
by Sebastian Koch
Received June 27, 2017
1295. BASEL_1
Basel Problem -- Preliminaries
by Artur Korni{\l}owicz and Karol P\kak
Received June 27, 2017
1296. BASEL_2
Basel Problem
by Karol P\kak and Artur Korni{\l}owicz
Received June 27, 2017
1297. ZMODLAT3
Dual Lattice of $\mathbb Z$-module Lattice
by Yuichi Futa and Yasunari Shidama
Received June 27, 2017
1298. VECTSP12
Isomorphism Theorem on Vector Spaces over a Ring
by Yuichi Futa and Yasunari Shidama
Received August 30, 2017
1299. DUALSP05
F. Riesz Theorem
by Keiko Narita, Kazuhisa Nakasho and Yasunari Shidama
Received August 30, 2017
1300. RING_5
On Roots of Polynomials and Algebraically Closed Fields
by Christoph Schwarzweller
Received August 30, 2017
1301. PELLS_EQ
The Pell's Equation
by Marcin Acewicz and Karol P\kak
Received August 30, 2017
1302. NOMIN_1
Simple named-complex valued nominative data -- definition and basic
operations
by Ievgen Ivanov, Mykola Nikitchenko, Andrii Kryvolap and Artur Korni{\l}owicz
Received August 30, 2017
1303. COUSIN2
Gauge Integral
by Roland Coghetto
Received September 3, 2017
1304. MESFUN11
Integral of Non Positive Functions
by Noboru Endou
Received September 3, 2017
1305. FUZIMPL1
Formal Introduction to Fuzzy Implications
by Adam Grabowski
Received September 3, 2017
1306. REALALG2
Formally Real Fields
by Christoph Schwarzweller
Received November 29, 2017
1307. FINANCE5
Introduction to Stopping Time in Stochastic Finance Theory: Part {II}
by Peter Jaeger
Received November 29, 2017
1308. NDIFF_8
Implicit Function Theorem -- Part {I}
by Kazuhisa Nakasho, Yuichi Futa and Yasunari Shidama
Received November 29, 2017
1309. DIOPHAN2
Introduction to {D}iophantine Approximation -- Part 2
by Yasushige Watase
Received November 29, 2017
1310. GTARSKI3
{T}arski Geometry Axioms -- Part {III}
by Roland Coghetto and Adam Grabowski
Received November 29, 2017
1311. HILB10_1
The {M}atiyasevich Theorem -- Preliminaries
by Karol P\kak
Received November 29, 2017
1312. FINANCE6
Introduction to Stochastic Finance: Random-Variables and Arbitrage Theory
by Peter Jaeger
Received March 27, 2018
1313. PARTPR_1
Kleene Algebra of Partial Predicates
by Artur Korni{\l}owicz, Ievgen Ivanov and Mykola Nikitchenko
Received March 27, 2018
1314. BKMODEL1
Beltrami-Klein Model, {P}art {I}
by Roland Coghetto
Received March 27, 2018
1315. BKMODEL2
Beltrami-Klein model, Part {II}
by Roland Coghetto
Received March 27, 2018
1316. MESFUN12
Fubini's Theorem for Nonnegative or Nonpositive Functions
by Noboru Endou
Received March 27, 2018
1317. MOEBIUS3
Sequences of Prime Reciprocals -- Preliminaries
by Adam Grabowski
Received March 27, 2018
1318. HILB10_2
Diophantine sets -- Preliminaries
by Karol P\kak
Received March 27, 2018