$S$-closed spaces
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- by Travis Thompson PDF
- Proc. Amer. Math. Soc. 60 (1976), 335-338 Request permission
Abstract:
A topological space X is said to be S-closed if and only if for every semiopen cover of X there exists a finite subfamily such that the union of their closures cover X. For a compact Hausdorff space, the concept of S-closed is shown to be equivalent to the concepts of extremally disconnected and projectiveness.References
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S. Gene Crossley and S. K. Hildebrand, Semi-closed sets and semi-continuity in topological spaces, Texas J. Sci. 22 (1971), 123-126.
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- Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199
- Norman Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36–41. MR 166752, DOI 10.2307/2312781
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 60 (1976), 335-338
- MSC: Primary 54D20; Secondary 54G05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0425899-0
- MathSciNet review: 0425899