Spaces with coarser minimal Hausdorff topologies

Porter, Jack; Vermeer, Johannes

doi:10.1090/S0002-9947-1985-0779052-1

Spaces with coarser minimal Hausdorff topologies
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by Jack Porter and Johannes Vermeer PDF

Trans. Amer. Math. Soc. 289 (1985), 59-71 Request permission

Abstract:

A technique is developed, using $H$-closed extensions, for determining when certain Hausdorff spaces are Katetov, i.e., have a coarser minimal Hausdorff topology. Our technique works for Čech-complete Lindelöf spaces, complete metrizable spaces, and many other spaces. Also, a number of interesting examples are presented; the most striking is an example of a Katetov space whose semiregularization is not Katetov.

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Expansions of

closed spaces

Closed subspaces of

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Projective elements in categories with perfect

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