Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998 Association of Mizar Users

Bounding Boxes for Special Sequences in $\calE^2$


Yatsuka Nakamura
Shinshu University, Nagano
Adam Grabowski
University of Bialystok
A part of this paper was written while the author visited the Shinshu University in the winter of 1997.

Summary.

This is the continuation of the proof of the Jordan Theorem according to [18].

MML Identifier: JORDAN5D

The terminology and notation used in this paper have been introduced in the following articles [19] [23] [2] [21] [20] [1] [16] [24] [3] [4] [22] [6] [11] [10] [9] [8] [12] [13] [15] [17] [7] [14] [5]

Contents (PDF format)

  1. Preliminaries
  2. Extrema of Projections
  3. Coordinates of the Special Circular Sequences Bounding Boxes

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski and Piotr Rudnicki. Bounding boxes for compact sets in $\calE^2$. Journal of Formalized Mathematics, 9, 1997.
[6] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[7] Agata Darmochwal. The Euclidean space. Journal of Formalized Mathematics, 3, 1991.
[8] Agata Darmochwal and Yatsuka Nakamura. The topological space $\calE^2_\rmT$. Arcs, line segments and special polygonal arcs. Journal of Formalized Mathematics, 3, 1991.
[9] Agata Darmochwal and Andrzej Trybulec. Similarity of formulae. Journal of Formalized Mathematics, 3, 1991.
[10] Katarzyna Jankowska. Matrices. Abelian group of matrices. Journal of Formalized Mathematics, 3, 1991.
[11] Jaroslaw Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Journal of Formalized Mathematics, 1, 1989.
[12] Jaroslaw Kotowicz and Yatsuka Nakamura. Introduction to Go-Board --- part I. Journal of Formalized Mathematics, 4, 1992.
[13] Jaroslaw Kotowicz and Yatsuka Nakamura. Introduction to Go-Board --- part II. Journal of Formalized Mathematics, 4, 1992.
[14] Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto. Preliminaries to circuits, I. Journal of Formalized Mathematics, 6, 1994.
[15] Yatsuka Nakamura and Andrzej Trybulec. Decomposing a Go-Board into cells. Journal of Formalized Mathematics, 7, 1995.
[16] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Journal of Formalized Mathematics, 5, 1993.
[17] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[18] Yukio Takeuchi and Yatsuka Nakamura. On the Jordan curve theorem. Technical Report 19804, Dept. of Information Eng., Shinshu University, 500 Wakasato, Nagano city, Japan, April 1980.
[19] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[20] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[21] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[22] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[23] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[24] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received June 8, 1998


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