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

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.