Lightly compact spaces and infra 𝐻-closed spaces

Hajek, Darrell W.; Todd, Aaron R.

doi:10.1090/S0002-9939-1975-0370499-3

Lightly compact spaces and infra $H$-closed spaces
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by Darrell W. Hajek and Aaron R. Todd PDF

Proc. Amer. Math. Soc. 48 (1975), 479-482 Request permission

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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Nicht alle ${T_2}$-minimalen Räume sind von 2 Kategorie

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