Original Research

A generalization of local connectedness in Topology

H. J. K. Ohlhoff, A. Verwey
Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie | Vol 1, No 4 | a1163 | DOI: https://doi.org/10.4102/satnt.v1i4.1163 | © 1982 H. J. K. Ohlhoff, A. Verwey | This work is licensed under CC Attribution 4.0
Submitted: 25 March 1982 | Published: 25 March 1982

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H. J. K. Ohlhoff,, South Africa
A. Verwey,, South Africa

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Abstract

Our aim in this paper is to obtain an acceptable generalization of the concept of locally connected spaces in Topology. This is done by utilizing the concept of E-connected spaces which was introduced by Preuss. Locally E-connected spaces are defined and results on locally connected spaces are generalized. In particular, it is shown that the class of all locally E-connected spaces determines a bicoreflective subcategory of Top. From the many examples that are available, we concentrate on those arising from the separation axioms.

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