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

## Preparing the Internal Approximations of Simple Closed Curves

Andrzej Trybulec
University of Bialystok

### Summary.

We mean by an internal approximation of a simple closed curve a special polygon disjoint with it but sufficiently close to it, i.e. such that it is clock-wise oriented and its right cells meet the curve. We prove lemmas used in the next article to construct a sequence of internal approximations.

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

#### MML Identifier: JORDAN11

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

Contents (PDF format)

#### 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. Countable sets and Hessenberg's theorem. Journal of Formalized Mathematics, 2, 1990.
[4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Gauges. Journal of Formalized Mathematics, 11, 1999.
[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] Agata Darmochwal and Yatsuka Nakamura. The topological space \$\calE^2_\rmT\$. Simple closed curves. Journal of Formalized Mathematics, 3, 1991.
[12] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[13] Katarzyna Jankowska. Matrices. Abelian group of matrices. Journal of Formalized Mathematics, 3, 1991.
[14] Yatsuka Nakamura and Andrzej Trybulec. Decomposing a Go-Board into cells. Journal of Formalized Mathematics, 7, 1995.
[15] Yatsuka Nakamura, Andrzej Trybulec, and Czeslaw Bylinski. Bounded domains and unbounded domains. Journal of Formalized Mathematics, 11, 1999.
[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] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[19] Andrzej Trybulec. More on external approximation of a continuum. Journal of Formalized Mathematics, 13, 2001.
[20] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[21] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[22] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.