Journal of Formalized Mathematics
Volume 11, 1999
University of Bialystok
Copyright (c) 1999 Association of Mizar Users

Properties of the External Approximation of Jordan's Curve


Artur Kornilowicz
University of Bialystok
This paper was written while the author visited Shinshu University, winter 1999.

MML Identifier: JORDAN10

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

Contents (PDF format)

  1. Properties of the External Approximation of Jordan's Curve

Acknowledgments

I would like to thank Professor Yatsuka Nakamura for his help in the preparation of the article.

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] Leszek Borys. Paracompact and metrizable spaces. Journal of Formalized Mathematics, 3, 1991.
[4] Czeslaw Bylinski. Gauges. Journal of Formalized Mathematics, 11, 1999.
[5] Czeslaw Bylinski and Piotr Rudnicki. Bounding boxes for compact sets in $\calE^2$. Journal of Formalized Mathematics, 9, 1997.
[6] Czeslaw Bylinski and Mariusz Zynel. Cages - the external approximation of Jordan's curve. Journal of Formalized Mathematics, 11, 1999.
[7] Agata Darmochwal. Compact spaces. 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] Stanislawa Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Journal of Formalized Mathematics, 2, 1990.
[13] Rafal Kwiatek. Factorial and Newton coefficients. Journal of Formalized Mathematics, 2, 1990.
[14] Yatsuka Nakamura and Czeslaw Bylinski. Extremal properties of vertices on special polygons, part 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] Yatsuka Nakamura, Andrzej Trybulec, and Czeslaw Bylinski. Bounded domains and unbounded domains. Journal of Formalized Mathematics, 11, 1999.
[17] Beata Padlewska. Connected spaces. Journal of Formalized Mathematics, 1, 1989.
[18] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[19] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[20] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[21] Andrzej Trybulec. Left and right component of the complement of a special closed curve. Journal of Formalized Mathematics, 7, 1995.
[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.

Received June 24, 1999


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