Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Spaces with coarser minimal Hausdorff topologies

Authors: Jack Porter and Johannes Vermeer
Journal: Trans. Amer. Math. Soc. 289 (1985), 59-71
MSC: Primary 54D25; Secondary 54D30, 54D35
MathSciNet review: 779052
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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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Keywords: Katetov spaces, minimal Hausdorff spaces, $ H$-closed extensions, absolutes
Article copyright: © Copyright 1985 American Mathematical Society