Vol. 38, No. 3, 1971

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Moore spaces and w Δ-spaces

Richard Earl Hodel

Vol. 38 (1971), No. 3, 641–652

This paper is a study of conditions under which a wΔ-space is a Moore space. In §2 we introduce the notion of a Gδdiagonal and show that every wΔ-space with a Gδ-diagonal is developable. In §3 we prove that every regular 𝜃-refinable wΔ-space with a point-countable separating open cover is a Moore space. In §4 we introduce the class of α-spaces and show that a regular wΔ-space is a Moore space if and only if it is an α-space. Finally, in §5 we study a new class of spaces which generalizes both semi-stratifiable and wΔ-spaces.

Mathematical Subject Classification 2000
Primary: 54D20
Secondary: 54E30
Received: 8 June 1970
Published: 1 September 1971
Richard Earl Hodel