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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A note on $ S$-closed spaces


Author: Asha Mathur
Journal: Proc. Amer. Math. Soc. 74 (1979), 350-352
MSC: Primary 54D20; Secondary 54G05
MathSciNet review: 524315
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Abstract: A topological space X is said to be S-closed if and only if for every semi-open cover of X there exists a finite subfamily such that the union of their closures cover X. For a Hausdorff space, the concept of S-closed is shown to be equivalent to the concept of extremally disconnected and nearly compact. Further it has been shown that EDH-closed spaces are precisely S-closed Hausdorff spaces.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0524315-0
PII: S 0002-9939(1979)0524315-0
Keywords: S-closed, extremally disconnected, nearly compact, EDH-closed
Article copyright: © Copyright 1979 American Mathematical Society