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Even Covering Properties and Somewhat Normal Spaces

Published online by Cambridge University Press:  20 November 2018

Hans-Peter Künzi and
Peter Fletcher
Hans-Peter Künzi
Affiliation:
Universität Bern Ch-3012, Bern Switzerland
Peter Fletcher
Affiliation:
Virginia Tech, Blacksburg Virginia 24061
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Abstract

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A topological space X is said to be somewhat normal provided that for each open cover is a normal cover of X. We show that a completely regular somewhat normal space need not be normal, thereby answering a question of W. M. Fleischman. We note that a collectionwise normal somewhat normal space need not be almost 2-fully normal, as had previously been asserted, and that neither the perfect image nor the perfect preimage of a somewhat normal space has to be somewhat normal.

Keywords

Primary54D18Secondary54D15

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 2 , 01 June 1986, pp. 154 - 159
Copyright
Copyright © Canadian Mathematical Society 1986

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