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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Lightly compact spaces and infra $H$-closed spaces

Authors: Darrell W. Hajek and Aaron R. Todd
Journal: Proc. Amer. Math. Soc. 48 (1975), 479-482
MSC: Primary 54D30
MathSciNet review: 0370499
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Abstract: We show that a topological space is lightly compact if and only if each countable open filter base has a cluster point. This gives a direct connection with $H$-closed spaces, and suggests the definition of infra $H$-closed spaces as those topological spaces whose continuous images in first countable Hausdorff spaces are closed. These properties are distinct and provide another characterization of pseudo-compact ${T_{{3^{1/2}}}}$ spaces.

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Keywords: Lightly compact spaces, open filter base, <IMG WIDTH="24" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$H$">-closed, absolutely closed, pseudocompact
Article copyright: © Copyright 1975 American Mathematical Society