Introduction to Go-Board --- Part I

Jaroslaw Kotowicz

Warsaw University, Bialystok

This article was written during my visit at Shinshu University in 1992.

Yatsuka Nakamura

Shinshu University, Nagano

Summary.

In the article we introduce Go-board as some kinds of matrix which elements belong to topological space ${\cal E}^2_{\rm T}$. We define the functor of delaying column in Go-board and relation between Go-board and finite sequence of point from ${\cal E}^2_{\rm T}$. Basic facts about those notations are proved. The concept of the article is based on [16].

MML Identifier: GOBOARD1

Contents (PDF format)

1. Real Numbers Preliminaries
2. Finite Sequences Preliminaries
3. Matrix Preliminaries
4. Basic Go-Board`s Notation

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.

[2] Grzegorz Bancerek. The fundamental properties of natural 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. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.

[6] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.

[7] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.

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

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

[10] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.

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

[12] Katarzyna Jankowska. Transpose matrices and groups of permutations. Journal of Formalized Mathematics, 4, 1992.

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

[14] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.

[15] Jan Popiolek. Some properties of functions modul and signum. Journal of Formalized Mathematics, 1, 1989.

[16] 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.

[17] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[18] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.

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

[20] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[21] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.