Vol. 57, No. 1, 1975

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Countable products of generalized countably compact spaces

Virgil Dwight House, Jr.

Vol. 57 (1975), No. 1, 183–197

In this paper two ways of generalizing compactness are studied. We may consider various types of refinements of open covers, such as countable open refinements, locally finite open refinements, etc. In another direction, countably compact spaces may be characterized as having the property that any sequence has a cluster point. Spaces which require that certain sequences have cluster points, such as Σ-spaces, wΔ-spaces, and q-spaces, will be referred to as generalized countably compact spaces.

Mathematical Subject Classification 2000
Primary: 54D20
Received: 5 April 1973
Published: 1 March 1975
Virgil Dwight House, Jr.