Vol. 30, No. 3, 1969

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A note on p-spaces and Moore spaces

Dennis K. Burke and R. A. Stoltenberg

Vol. 30 (1969), No. 3, 601–608

In this note we investigate p-spaces and their relationship to Moore spaces. Specifically, it is shown that among p-spaces Moore spaces are equivalent to semi-metric spaces and spaces with a σ-discrete network. A certain class of p-spaces, called strict p-spaces, is given an internal characterization and this is used to show that a pointwise paracompact p-space with a point-countable base is a pointwise paracompact Moore space.

Mathematical Subject Classification
Primary: 54.50
Received: 9 October 1968
Published: 1 September 1969
Dennis K. Burke
R. A. Stoltenberg