Vol. 71, No. 2, 1977

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On wΔ-spaces, -spaces and Σ-spaces

Peter Fletcher and William Lindgren

Vol. 71 (1977), No. 2, 419–428

One of the reasons that paracompactness plays a central role in general topology is that it is a property shared by compact spaces and metric spaces. Recently there has been considerable interest in topological properties shared by countably compact spaces and metric spaces. R. W. Heath has introduced a method of describing a generalized metric property of a topological space (X,τ) by means of a function g : N × X τ and R. E. Hodel has modified this method to obtain important new classes of spaces. Subsequently, J. Nagata obtained a similar characterization of Σ#-spaces, and it now appears that the method of Heath and Hodel provides an opportunity to clarify the relationships among those properties that are shared by countably compact spaces and metric spaces. This note seeks to establish some relationships among these properties.

Mathematical Subject Classification 2000
Primary: 54D30
Secondary: 54E20
Received: 31 May 1976
Revised: 2 August 1976
Published: 1 August 1977
Peter Fletcher
William Lindgren