Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Locally Connected Spaces
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Beata Padlewska
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Technical University of Bialystok
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Supported by RPBP.III-24.C1.
Summary.
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This article is a continuation of [3].
We define a neighbourhood of a point and a neighbourhood of a set and
prove some facts about them. Then the definitions of a locally connected
space and a locally connected set are introduced. Some theorems about
locally connected spaces are given (based on [2]).
We also define
a quasi-component of a point and prove some of its basic properties.
The terminology and notation used in this paper have been
introduced in the following articles
[5]
[6]
[4]
[7]
[3]
[1]
Contents (PDF format)
Bibliography
- [1]
Agata Darmochwal.
Compact spaces.
Journal of Formalized Mathematics,
1, 1989.
- [2]
Kazimierz Kuratowski.
\em Wstep do teorii mnogosci i topologii.
PWN, War\-sza\-wa, 1977.
- [3]
Beata Padlewska.
Connected spaces.
Journal of Formalized Mathematics,
1, 1989.
- [4]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
Journal of Formalized Mathematics,
1, 1989.
- [5]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
- [6]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [7]
Miroslaw Wysocki and Agata Darmochwal.
Subsets of topological spaces.
Journal of Formalized Mathematics,
1, 1989.
Received September 5, 1990
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