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Proceedings of the American Mathematical Society

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

 

 

Properties of $ S$-closed spaces


Author: Douglas E. Cameron
Journal: Proc. Amer. Math. Soc. 72 (1978), 581-586
MSC: Primary 54D30; Secondary 54G05
MathSciNet review: 0514999
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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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DOI: https://doi.org/10.1090/S0002-9939-1978-0514999-4
Keywords: S-closed, regular closed, extremally disconnected, semiopen, maximal topologies
Article copyright: © Copyright 1978 American Mathematical Society