More on the Finite Sequences on the Plane

Andrzej Trybulec

University of Bialystok

Summary.

We continue proving lemmas needed for the proof of the Jordan curve theorem. The main goal was to prove the last theorem being a mutation of the first theorem in [12].

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

MML Identifier: TOPREAL8

Contents (PDF format)

1. Preliminaries
2. Finite Sequences
3. On the Plane

Bibliography

[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] Jozef Bialas. Group and field definitions. Journal of Formalized Mathematics, 1, 1989.

[4] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[5] Czeslaw Bylinski. Some properties of restrictions of finite sequences. Journal of Formalized Mathematics, 7, 1995.

[6] Agata Darmochwal. The Euclidean space. Journal of Formalized Mathematics, 3, 1991.

[7] Agata Darmochwal and Yatsuka Nakamura. The topological space $\calE^2_\rmT$. Arcs, line segments and special polygonal arcs. Journal of Formalized Mathematics, 3, 1991.

[8] Katarzyna Jankowska. Matrices. Abelian group of matrices. Journal of Formalized Mathematics, 3, 1991.

[9] Jaroslaw Kotowicz. Monotone real sequences. Subsequences. Journal of Formalized Mathematics, 1, 1989.

[10] Jaroslaw Kotowicz. Functions and finite sequences of real numbers. Journal of Formalized Mathematics, 5, 1993.

[11] Jaroslaw Kotowicz and Yatsuka Nakamura. Introduction to Go-Board --- part I. Journal of Formalized Mathematics, 4, 1992.

[12] Jaroslaw Kotowicz and Yatsuka Nakamura. Properties of Go-Board --- part III. Journal of Formalized Mathematics, 4, 1992.

[13] Yatsuka Nakamura and Piotr Rudnicki. Vertex sequences induced by chains. Journal of Formalized Mathematics, 7, 1995.

[14] Yatsuka Nakamura and Andrzej Trybulec. Decomposing a Go-Board into cells. Journal of Formalized Mathematics, 7, 1995.

[15] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Journal of Formalized Mathematics, 5, 1993.

[16] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.

[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. On the decomposition of finite sequences. Journal of Formalized Mathematics, 7, 1995.

[20] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.

[21] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.