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New characterisations of pseudocompact spaces

Published online by Cambridge University Press:  17 April 2009

Wang Yan-Min
Wang Yan-Min
Affiliation:
Department of Basic Sciences, Shanghai Institute of Mechanical Engineering, Shanghai, Peoples Republic of China
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Abstract

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In this paper, we give a new characterisation of pseudo-compact spaces, namely a space X is pseudocompact if and only if each σ-point finite open cover of X has a finite subfamily whose union is dense. As a corollary, we show that every pseudocompact σ-metacompact (or screenable) space is compact, which sharpens some known results.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 2 , October 1988 , pp. 293 - 298
Copyright
Copyright © Australian Mathematical Society 1988

References

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