Bulletin of the Australian Mathematical Society

Research Article

New characterisations of pseudocompact spaces

Wang Yan-Mina1

a1 Department of Basic Sciences, Shanghai Institute of Mechanical Engineering, Shanghai, Peoples Republic of China

Abstract

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.

(Received December 11 1987)