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

## Locally Connected Spaces

Technical University of Bialystok
Supported by RPBP.III-24.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 quasi-component of a point and prove some of its basic properties.

#### MML Identifier: CONNSP_2

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.