Volume 10, 1998

University of Bialystok

Copyright (c) 1998 Association of Mizar Users

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

- This is the continuation of the proof of the Jordan Theorem according to [18].

- Preliminaries
- Extrema of Projections
- Coordinates of the Special Circular Sequences Bounding Boxes

- [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]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [5]
Czeslaw Bylinski and Piotr Rudnicki.
Bounding boxes for compact sets in $\calE^2$.
*Journal of Formalized Mathematics*, 9, 1997. - [6]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Agata Darmochwal.
The Euclidean space.
*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]
Agata Darmochwal and Andrzej Trybulec.
Similarity of formulae.
*Journal of Formalized Mathematics*, 3, 1991. - [10]
Katarzyna Jankowska.
Matrices. Abelian group of matrices.
*Journal of Formalized Mathematics*, 3, 1991. - [11]
Jaroslaw Kotowicz.
Convergent real sequences. Upper and lower bound of sets of real numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [12]
Jaroslaw Kotowicz and Yatsuka Nakamura.
Introduction to Go-Board --- part I.
*Journal of Formalized Mathematics*, 4, 1992. - [13]
Jaroslaw Kotowicz and Yatsuka Nakamura.
Introduction to Go-Board --- part II.
*Journal of Formalized Mathematics*, 4, 1992. - [14]
Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto.
Preliminaries to circuits, I.
*Journal of Formalized Mathematics*, 6, 1994. - [15]
Yatsuka Nakamura and Andrzej Trybulec.
Decomposing a Go-Board into cells.
*Journal of Formalized Mathematics*, 7, 1995. - [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] 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.
- [19]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [20]
Andrzej Trybulec.
Tuples, projections and Cartesian products.
*Journal of Formalized Mathematics*, 1, 1989. - [21]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [22]
Wojciech A. Trybulec.
Pigeon hole principle.
*Journal of Formalized Mathematics*, 2, 1990. - [23]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [24]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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