Journal of Formalized Mathematics
Volume 14, 2002
University of Bialystok
Copyright (c) 2002 Association of Mizar Users

Introducing Spans


Andrzej Trybulec
University of Bialystok

Summary.

A sequence of internal approximations of simple closed curves is introduced. They are called spans.

This work has been partially supported by CALCULEMUS grant HPRN-CT-2000-00102.

MML Identifier: JORDAN13

The terminology and notation used in this paper have been introduced in the following articles [20] [17] [26] [3] [23] [2] [18] [27] [5] [6] [1] [4] [7] [25] [13] [14] [19] [10] [11] [12] [15] [16] [24] [8] [9] [21] [22]

Contents (PDF format)

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[8] Czeslaw Bylinski. Gauges. Journal of Formalized Mathematics, 11, 1999.
[9] Czeslaw Bylinski. Some properties of cells on go board. Journal of Formalized Mathematics, 11, 1999.
[10] Agata Darmochwal. The Euclidean space. Journal of Formalized Mathematics, 3, 1991.
[11] Agata Darmochwal and Yatsuka Nakamura. The topological space $\calE^2_\rmT$. Arcs, line segments and special polygonal arcs. Journal of Formalized Mathematics, 3, 1991.
[12] Agata Darmochwal and Yatsuka Nakamura. The topological space $\calE^2_\rmT$. Simple closed curves. Journal of Formalized Mathematics, 3, 1991.
[13] Katarzyna Jankowska. Matrices. Abelian group of matrices. Journal of Formalized Mathematics, 3, 1991.
[14] Stanislawa Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Journal of Formalized Mathematics, 2, 1990.
[15] Jaroslaw Kotowicz and Yatsuka Nakamura. Introduction to Go-Board --- part I. Journal of Formalized Mathematics, 4, 1992.
[16] Yatsuka Nakamura and Czeslaw Bylinski. Extremal properties of vertices on special polygons, part I. Journal of Formalized Mathematics, 6, 1994.
[17] Yatsuka Nakamura and Andrzej Trybulec. Decomposing a Go-Board into cells. Journal of Formalized Mathematics, 7, 1995.
[18] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Journal of Formalized Mathematics, 5, 1993.
[19] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[20] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[21] Andrzej Trybulec. More on external approximation of a continuum. Journal of Formalized Mathematics, 13, 2001.
[22] Andrzej Trybulec. Preparing the internal approximations of simple closed curves. Journal of Formalized Mathematics, 14, 2002.
[23] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[24] Andrzej Trybulec and Yatsuka Nakamura. On the order on a special polygon. Journal of Formalized Mathematics, 9, 1997.
[25] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[26] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[27] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received May 27, 2002


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