Properties of 𝑆-closed spaces

Cameron, Douglas E.

doi:10.1090/S0002-9939-1978-0514999-4

Properties of $S$-closed spaces
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by Douglas E. Cameron

Proc. Amer. Math. Soc. 72 (1978), 581-586

DOI: https://doi.org/10.1090/S0002-9939-1978-0514999-4

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Abstract:

It is shown that the S-closed spaces introduced by Travis Thompson using semiopen sets may be characterized as spaces where covers by regular closed sets have finite subcovers. S-closed is contagious and semiregular but is neither productive nor preserved by continuous surjections. Extremally disconnected QHC spaces are S-closed and maximal S-closed spaces are precisely the maximal QHC spaces which are extremally disconnected.

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