Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Locally Connected Spaces

Beata Padlewska

Technical University of Bialystok

Supported by RPBP.III24.C1.
Summary.

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 quasicomponent 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
[
Download a postscript version,
MML identifier index,
Mizar home page]