Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998 Association of Mizar Users

The Definition and Basic Properties of Topological Groups


Artur Kornilowicz
University of Bialystok

MML Identifier: TOPGRP_1

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

Contents (PDF format)

  1. Preliminaries
  2. On the Groups
  3. On the Topological Spaces
  4. The Group of Homeomorphisms
  5. On the Topological Groups

Bibliography

[1] Jozef Bialas and Yatsuka Nakamura. Dyadic numbers and T$_4$ topological spaces. Journal of Formalized Mathematics, 7, 1995.
[2] Leszek Borys. Paracompact and metrizable spaces. Journal of Formalized Mathematics, 3, 1991.
[3] Czeslaw Bylinski. Binary operations. 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. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[8] Agata Darmochwal. Compact spaces. Journal of Formalized Mathematics, 1, 1989.
[9] Agata Darmochwal. Families of subsets, subspaces and mappings in topological spaces. Journal of Formalized Mathematics, 1, 1989.
[10] Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski. Abelian groups, fields and vector spaces. Journal of Formalized Mathematics, 1, 1989.
[11] Michal Muzalewski. Categories of groups. Journal of Formalized Mathematics, 3, 1991.
[12] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[13] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[14] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Journal of Formalized Mathematics, 7, 1995.
[15] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[16] Andrzej Trybulec. A Borsuk theorem on homotopy types. Journal of Formalized Mathematics, 3, 1991.
[17] Andrzej Trybulec. Baire spaces, Sober spaces. Journal of Formalized Mathematics, 9, 1997.
[18] Wojciech A. Trybulec. Groups. Journal of Formalized Mathematics, 2, 1990.
[19] Wojciech A. Trybulec. Subgroup and cosets of subgroups. Journal of Formalized Mathematics, 2, 1990.
[20] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[21] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[22] Miroslaw Wysocki and Agata Darmochwal. Subsets of topological spaces. Journal of Formalized Mathematics, 1, 1989.
[23] Mariusz Zynel and Adam Guzowski. \Tzero\ topological spaces. Journal of Formalized Mathematics, 6, 1994.

Received September 7, 1998


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