Gauges and Cages. Part I

Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000 Association of Mizar Users

Gauges and Cages. Part I

Artur Kornilowicz: University of Bialystok
Robert Milewski: University of Bialystok
Adam Naumowicz: University of Bialystok
Andrzej Trybulec: University of Bialystok

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

MML Identifier: JORDAN1A

The terminology and notation used in this paper have been introduced in the following articles [29] [32] [2] [30] [13] [1] [4] [5] [3] [31] [24] [19] [26] [25] [9] [18] [14] [27] [17] [15] [10] [16] [11] [12] [7] [20] [28] [21] [22] [6] [8] [23]

Contents (PDF format)

Preliminaries
Some Subsets of the Plane
Goboards
Gauges
Cages

Bibliography

[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. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.

[6] Czeslaw Bylinski. Gauges. Journal of Formalized Mathematics, 11, 1999.

[7] Czeslaw Bylinski and Piotr Rudnicki. Bounding boxes for compact sets in $\calE^2$. Journal of Formalized Mathematics, 9, 1997.

[8] Czeslaw Bylinski and Mariusz Zynel. Cages - the external approximation of Jordan's curve. Journal of Formalized Mathematics, 11, 1999.

[9] Agata Darmochwal. Compact spaces. Journal of Formalized Mathematics, 1, 1989.

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

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

[12] Agata Darmochwal and Yatsuka Nakamura. The topological space $\calE^2_\rmT$. Simple closed curves. Journal of Formalized Mathematics, 3, 1991.

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

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

[15] Stanislawa Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Journal of Formalized Mathematics, 2, 1990.

[16] Andrzej Kondracki. The Chinese Remainder Theorem. Journal of Formalized Mathematics, 9, 1997.

[17] Jaroslaw Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Journal of Formalized Mathematics, 1, 1989.

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

[19] Rafal Kwiatek. Factorial and Newton coefficients. Journal of Formalized Mathematics, 2, 1990.

[20] Yatsuka Nakamura and Czeslaw Bylinski. Extremal properties of vertices on special polygons, part I. Journal of Formalized Mathematics, 6, 1994.

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

[22] Yatsuka Nakamura and Andrzej Trybulec. A decomposition of simple closed curves and the order of their points. Journal of Formalized Mathematics, 9, 1997.

[23] Yatsuka Nakamura, Andrzej Trybulec, and Czeslaw Bylinski. Bounded domains and unbounded domains. Journal of Formalized Mathematics, 11, 1999.

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

[25] Beata Padlewska. Connected spaces. Journal of Formalized Mathematics, 1, 1989.

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

[27] Konrad Raczkowski and Pawel Sadowski. Topological properties of subsets in real numbers. Journal of Formalized Mathematics, 2, 1990.

[28] Piotr Rudnicki and Andrzej Trybulec. Abian's fixed point theorem. Journal of Formalized Mathematics, 9, 1997.

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

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

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

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

Received September 12, 2000

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