Semicontinuous and irresolute images of $S$-closed spaces
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- by Travis Thompson
- Proc. Amer. Math. Soc. 66 (1977), 359-362
- DOI: https://doi.org/10.1090/S0002-9939-1977-0451193-9
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Abstract:
A topological space is S-closed if and only if every semi-open cover of X has a finite subcollection whose closures cover X. The images of S-closed spaces under various mappings are investigated culminating in this main result: A Hausdorff space X is S-closed if and only if the irresolute image of X in any Hausdorff space is closed.References
- S. Gene Crossley and S. K. Hildebrand, Semi-closed sets and semi-continuity in topological spaces, Texas J. Sci. 22 (1971), 123-126.
—, Semi-closure, Texas J. Sci. 22 (1971), 99-112.
- S. Gene Crossley and S. K. Hildebrand, Semi-topological properties, Fund. Math. 74 (1972), no. 3, 233–254. MR 301690, DOI 10.4064/fm-74-3-233-254
- James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606 T. R. Hamlett, Semi-continuous and irresolute functions, Texas Academy of Science, Vol. 27, Nos. 1, 2.
- Yoshinori Isomichi, New concepts in the theory of topological space—supercondensed set, subcondensed set, and condensed set, Pacific J. Math. 38 (1971), 657–668. MR 310821, DOI 10.2140/pjm.1971.38.657
- Norman Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36–41. MR 166752, DOI 10.2307/2312781
- Travis Thompson, $S$-closed spaces, Proc. Amer. Math. Soc. 60 (1976), 335–338 (1977). MR 425899, DOI 10.1090/S0002-9939-1976-0425899-0
- Stephen Willard, General topology, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1970. MR 0264581
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 66 (1977), 359-362
- MSC: Primary 54C10
- DOI: https://doi.org/10.1090/S0002-9939-1977-0451193-9
- MathSciNet review: 0451193