Journal of Formalized Mathematics
Volume 9, 1997
University of Bialystok
Copyright (c) 1997 Association of Mizar Users

## On the Order on a Special Polygon

Andrzej Trybulec
University of Bialystok
Yatsuka Nakamura
Shinshu University, Nagano

### Summary.

The goal of the article is to determine the order of the special points defined in [7] on a special polygon. We restrict ourselves to the clockwise oriented finite sequences (the concept defined in this article) that start in N-min C (C being a compact non empty subset of the plane).

#### MML Identifier: SPRECT_2

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

#### Contents (PDF format)

1. Preliminaries
2. On the finite sequences
3. Compact subsets of the plane
4. Finite sequences on the plane
5. The area of a sequence
6. Horizontal and vertical connections
7. Orientation
8. Appending corners
9. The order

#### 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] Jozef Bialas. Group and field definitions. 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 and Piotr Rudnicki. Bounding boxes for compact sets in \$\calE^2\$. Journal of Formalized Mathematics, 9, 1997.
[8] Agata Darmochwal. Compact spaces. Journal of Formalized Mathematics, 1, 1989.
[9] Agata Darmochwal. The Euclidean space. Journal of Formalized Mathematics, 3, 1991.
[10] Agata Darmochwal and Yatsuka Nakamura. The topological space \$\calE^2_\rmT\$. Arcs, line segments and special polygonal arcs. Journal of Formalized Mathematics, 3, 1991.
[11] Jaroslaw Kotowicz and Yatsuka Nakamura. Introduction to Go-Board --- part I. Journal of Formalized Mathematics, 4, 1992.
[12] Yatsuka Nakamura and Roman Matuszewski. Reconstructions of special sequences. Journal of Formalized Mathematics, 8, 1996.
[13] Yatsuka Nakamura and Andrzej Trybulec. Decomposing a Go-Board into cells. Journal of Formalized Mathematics, 7, 1995.
[14] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Journal of Formalized Mathematics, 5, 1993.
[15] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[16] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[17] Andrzej Trybulec. On the decomposition of finite sequences. Journal of Formalized Mathematics, 7, 1995.
[18] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[19] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[20] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.