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

Components and Basis of Topological Spaces


Robert Milewski
University in Bialystok

Summary.

This article contains many facts about components and basis of topological spaces.

This work has been supported by KBN Grant 8 T11C 018 12.

MML Identifier: YELLOW15

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

Contents (PDF format)

  1. Preliminaries
  2. Components
  3. About Basis of Topological Spaces

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. K\"onig's theorem. Journal of Formalized Mathematics, 2, 1990.
[3] Grzegorz Bancerek. Bounds in posets and relational substructures. Journal of Formalized Mathematics, 8, 1996.
[4] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Journal of Formalized Mathematics, 8, 1996.
[5] Grzegorz Bancerek. The ``way-below'' relation. Journal of Formalized Mathematics, 8, 1996.
[6] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[7] Jozef Bialas. Group and field definitions. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[9] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[10] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[11] Czeslaw Bylinski. A classical first order language. Journal of Formalized Mathematics, 2, 1990.
[12] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[13] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[14] Robert Milewski. Algebraic lattices. Journal of Formalized Mathematics, 8, 1996.
[15] Robert Milewski. Bases of continuous lattices. Journal of Formalized Mathematics, 10, 1998.
[16] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[17] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[18] Konrad Raczkowski and Pawel Sadowski. Equivalence relations and classes of abstraction. Journal of Formalized Mathematics, 1, 1989.
[19] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Journal of Formalized Mathematics, 7, 1995.
[20] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[21] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[22] Wojciech A. Trybulec. Groups. Journal of Formalized Mathematics, 2, 1990.
[23] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[24] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[25] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[26] Edmund Woronowicz. Many-argument relations. Journal of Formalized Mathematics, 2, 1990.

Received June 22, 1999


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