Volume 9, 1997

University of Bialystok

Copyright (c) 1997 Association of Mizar Users

**Adam Grabowski**- University of Bialystok
- This paper was written while the author visited the Shinshu University in the winter of 1997.
**Yatsuka Nakamura**- Shinshu University, Nagano

- The proof of the Jordan Curve Theorem according to [11] is continued. The notions of the first and last point of a oriented arc are introduced as well as ordering of points on a curve in $\calE^2_T$.

- First and last point of a curve
- The ordering of points on a curve
- Some properties of the ordering of points on a curve

- [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.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [5]
Agata Darmochwal.
Families of subsets, subspaces and mappings in topological spaces.
*Journal of Formalized Mathematics*, 1, 1989. - [6]
Agata Darmochwal.
The Euclidean space.
*Journal of Formalized Mathematics*, 3, 1991. - [7]
Agata Darmochwal and Yatsuka Nakamura.
Metric spaces as topological spaces --- fundamental concepts.
*Journal of Formalized Mathematics*, 3, 1991. - [8]
Agata Darmochwal and Yatsuka Nakamura.
The topological space $\calE^2_\rmT$. Arcs, line segments and special polygonal arcs.
*Journal of Formalized Mathematics*, 3, 1991. - [9]
Yatsuka Nakamura and Roman Matuszewski.
Reconstructions of special sequences.
*Journal of Formalized Mathematics*, 8, 1996. - [10]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
*Journal of Formalized Mathematics*, 1, 1989. - [11] Yukio Takeuchi and Yatsuka Nakamura. On the Jordan curve theorem. Technical Report 19804, Dept. of Information Eng., Shinshu University, 500 Wakasato, Nagano city, Japan, April 1980.
- [12]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [13]
Wojciech A. Trybulec.
Pigeon hole principle.
*Journal of Formalized Mathematics*, 2, 1990. - [14]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [15]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

[ Download a postscript version, MML identifier index, Mizar home page]