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On semi-regularization topologies

Part of: Maps and general types of spaces defined by maps Fairly general properties Generalities

Published online by Cambridge University Press:  09 April 2009

M. Mršević ,
I. L. Reilly  and
M. K. Vamanamurthy
M. Mršević
Affiliation:
Institute of Mathematics Faculty of Sciences University of Belgrade, Yugoslavia
I. L. Reilly
Affiliation:
Department of Mathematics & Statistics University of Auckland, New Zealand
M. K. Vamanamurthy
Affiliation:
Department of Mathematics & Statistics University of Auckland, New Zealand
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Abstract

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This paper discusses several properties of topological spaces and how they are refelected by corresponding properties of the associated semi-regularization topologies. For example a space is almost locally connected if and only if its semi-regularization is locally connected. Various separation, connectedness, covering, and mapping properties are considered.

Keywords

semi-regularregular openalmost regularalmost locally connectednearly compactalmost continuousδ-continuoussuper-constinuous.

MSC classification

Secondary: 54A10: Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 54C10: Special maps on topological spaces (open, closed, perfect, etc.) 54D05: Connected and locally connected spaces (general aspects) 54D10: Lower separation axioms ($T_0$--$T_3$, etc.) 54D30: Compactness
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 1 , February 1985 , pp. 40 - 54
Copyright
Copyright © Australian Mathematical Society 1985

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