Vol. 32, No. 3, 1970

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The compactness of countably compact spaces

Philip Bacon

Vol. 32 (1970), No. 3, 587–592

By a countably compact space we mean a topological space every countable open cover of which contains a finite subcover. It is known that a countably compact space is compact if it is either a Moore space or a paracompact space. In the first section of this note we introduce a class of topological spaces that includes all Moore spaces and all paracompact spaces but includes no space that is countably compact and not compact. In the second section we study the class of those spaces in which closed countably compact subsets are always compact.

Mathematical Subject Classification
Primary: 54.40
Received: 31 March 1969
Revised: 15 August 1969
Published: 1 March 1970
Philip Bacon