Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996 Association of Mizar Users

## The First Part of Jordan's Theorem for Special Polygons

Yatsuka Nakamura
Shinshu University, Nagano
Andrzej Trybulec
Warsaw University, Bialystok

### Summary.

We prove here the first part of Jordan's theorem for special polygons, i.e., the complement of a special polygon is the union of two components (a left component and a right component). At this stage, we do not know if the two components are different from each other.

#### MML Identifier: GOBRD12

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

Contents (PDF format)

#### Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[5] Agata Darmochwal. The Euclidean space. Journal of Formalized Mathematics, 3, 1991.
[6] Agata Darmochwal and Yatsuka Nakamura. The topological space \$\calE^2_\rmT\$. Arcs, line segments and special polygonal arcs. Journal of Formalized Mathematics, 3, 1991.
[7] Katarzyna Jankowska. Matrices. Abelian group of matrices. Journal of Formalized Mathematics, 3, 1991.
[8] Jaroslaw Kotowicz and Yatsuka Nakamura. Introduction to Go-Board --- part I. Journal of Formalized Mathematics, 4, 1992.
[9] Jaroslaw Kotowicz and Yatsuka Nakamura. Introduction to Go-Board --- part II. Journal of Formalized Mathematics, 4, 1992.
[10] Yatsuka Nakamura and Andrzej Trybulec. Decomposing a Go-Board into cells. Journal of Formalized Mathematics, 7, 1995.
[11] Yatsuka Nakamura and Andrzej Trybulec. Adjacency concept for pairs of natural numbers. Journal of Formalized Mathematics, 8, 1996.
[12] Yatsuka Nakamura and Andrzej Trybulec. Components and unions of components. Journal of Formalized Mathematics, 8, 1996.
[13] Beata Padlewska. Connected spaces. Journal of Formalized Mathematics, 1, 1989.
[14] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[15] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[16] Andrzej Trybulec. Left and right component of the complement of a special closed curve. Journal of Formalized Mathematics, 7, 1995.
[17] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[18] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[19] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[20] Miroslaw Wysocki and Agata Darmochwal. Subsets of topological spaces. Journal of Formalized Mathematics, 1, 1989.

Received July 22, 1996

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