Journal of Formalized Mathematics
Volume 13, 2001
University of Bialystok
Copyright (c) 2001 Association of Mizar Users

Upper and Lower Sequence of a Cage


Robert Milewski
University of Bialystok

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

MML Identifier: JORDAN1E

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

Contents (PDF format)

  1. Preliminaries
  2. About Upper and Lower Sequence of a Cage

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 properties of restrictions of finite sequences. Journal of Formalized Mathematics, 7, 1995.
[6] Czeslaw Bylinski and Piotr Rudnicki. Bounding boxes for compact sets in $\calE^2$. Journal of Formalized Mathematics, 9, 1997.
[7] Czeslaw Bylinski and Mariusz Zynel. Cages - the external approximation of Jordan's curve. Journal of Formalized Mathematics, 11, 1999.
[8] Agata Darmochwal. Compact spaces. Journal of Formalized Mathematics, 1, 1989.
[9] Agata Darmochwal. The Euclidean space. Journal of Formalized Mathematics, 3, 1991.
[10] Agata Darmochwal and Yatsuka Nakamura. The topological space $\calE^2_\rmT$. Arcs, line segments and special polygonal arcs. Journal of Formalized Mathematics, 3, 1991.
[11] Agata Darmochwal and Yatsuka Nakamura. The topological space $\calE^2_\rmT$. Simple closed curves. Journal of Formalized Mathematics, 3, 1991.
[12] Katarzyna Jankowska. Matrices. Abelian group of matrices. Journal of Formalized Mathematics, 3, 1991.
[13] Yatsuka Nakamura and Czeslaw Bylinski. Extremal properties of vertices on special polygons, part I. Journal of Formalized Mathematics, 6, 1994.
[14] Yatsuka Nakamura and Roman Matuszewski. Reconstructions of special sequences. Journal of Formalized Mathematics, 8, 1996.
[15] Yatsuka Nakamura and Piotr Rudnicki. Vertex sequences induced by chains. Journal of Formalized Mathematics, 7, 1995.
[16] Beata Padlewska. Connected spaces. 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] Andrzej Trybulec and Yatsuka Nakamura. On the order on a special polygon. Journal of Formalized Mathematics, 9, 1997.
[21] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.

Received August 8, 2001


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