Vol. 44, No. 2, 1973

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Gδ-diagonals and metrization theorems

William George McArthur

Vol. 44 (1973), No. 2, 613–617
Abstract

The topological space X is said to have a Gδ-diagonal if the diagonal Δ = {(x,x) : x X} is a Gδ-set in X ×X. It is easy to see that if X has a coarser metrizable topology, then X has a Gδ-diagonal. The main result is that a completely regular pseudocompact space with a regular Gδ-diagonal is metrizable.

Mathematical Subject Classification 2000
Primary: 54E35
Milestones
Received: 29 October 1971
Published: 1 February 1973
Authors
William George McArthur