Volume 14, 2002

University of Bialystok

Copyright (c) 2002 Association of Mizar Users

**Andrzej Trybulec**- University of Bialystok
- This work has been partially supported by CALCULEMUS grant HPRN-CT-2000-00102. The work has been done while the author visited Shinshu University.
**Yatsuka Nakamura**- Shinshu University, Nagano

- The purpose of the paper is to prove lemmas needed for the Jordan curve theorem. The main result is that the decomposition of a simple closed curve into two arcs with the ends $p_1, p_2$ is unique in the sense that every arc on the curve with the same ends must be equal to one of them.

Contents (PDF format)

- [1]
Grzegorz Bancerek.
The ordinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [2]
Leszek Borys.
Paracompact and metrizable spaces.
*Journal of Formalized Mathematics*, 3, 1991. - [3]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [4]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [5]
Czeslaw Bylinski.
Partial functions.
*Journal of Formalized Mathematics*, 1, 1989. - [6]
Czeslaw Bylinski and Piotr Rudnicki.
Bounding boxes for compact sets in $\calE^2$.
*Journal of Formalized Mathematics*, 9, 1997. - [7]
Agata Darmochwal.
Compact spaces.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
Agata Darmochwal.
Families of subsets, subspaces and mappings in topological spaces.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [10]
Agata Darmochwal.
The Euclidean space.
*Journal of Formalized Mathematics*, 3, 1991. - [11]
Agata Darmochwal and Yatsuka Nakamura.
Metric spaces as topological spaces --- fundamental concepts.
*Journal of Formalized Mathematics*, 3, 1991. - [12]
Agata Darmochwal and Yatsuka Nakamura.
The topological space $\calE^2_\rmT$. Arcs, line segments and special polygonal arcs.
*Journal of Formalized Mathematics*, 3, 1991. - [13]
Agata Darmochwal and Yatsuka Nakamura.
The topological space $\calE^2_\rmT$. Simple closed curves.
*Journal of Formalized Mathematics*, 3, 1991. - [14]
Adam Grabowski and Yatsuka Nakamura.
The ordering of points on a curve. Part II.
*Journal of Formalized Mathematics*, 9, 1997. - [15]
Zbigniew Karno.
Continuity of mappings over the union of subspaces.
*Journal of Formalized Mathematics*, 4, 1992. - [16]
Yatsuka Nakamura.
On the dividing function of the simple closed curve into segments.
*Journal of Formalized Mathematics*, 10, 1998. - [17]
Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto.
Preliminaries to circuits, I.
*Journal of Formalized Mathematics*, 6, 1994. - [18]
Yatsuka Nakamura and Andrzej Trybulec.
A decomposition of simple closed curves and the order of their points.
*Journal of Formalized Mathematics*, 9, 1997. - [19]
Yatsuka Nakamura, Andrzej Trybulec, and Czeslaw Bylinski.
Bounded domains and unbounded domains.
*Journal of Formalized Mathematics*, 11, 1999. - [20]
Beata Padlewska.
Locally connected spaces.
*Journal of Formalized Mathematics*, 2, 1990. - [21]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
*Journal of Formalized Mathematics*, 1, 1989. - [22]
Konrad Raczkowski and Pawel Sadowski.
Real function continuity.
*Journal of Formalized Mathematics*, 2, 1990. - [23]
Konrad Raczkowski and Pawel Sadowski.
Topological properties of subsets in real numbers.
*Journal of Formalized Mathematics*, 2, 1990. - [24]
Andrzej Trybulec.
Enumerated sets.
*Journal of Formalized Mathematics*, 1, 1989. - [25]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [26]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [27]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [28]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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