$S$-sets and $S$-perfect mappings
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- by R. F. Dickman and R. L. Krystock PDF
- Proc. Amer. Math. Soc. 80 (1980), 687-692 Request permission
Abstract:
In this note we generalize the notion of an S-closed space to S-sets of a space. Among our characterizations of S-sets, we show that a subset A of an extremally disconnected space X is an S-set in X if and only if A is an H-set in X. We also investigate conditions under which mappings or their inverses preserve S-sets.References
- S. Gene Crossley and S. K. Hildebrand, Semi-topological properties, Fund. Math. 74 (1972), no.Β 3, 233β254. MR 301690, DOI 10.4064/fm-74-3-233-254
- 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, DOI 10.1007/978-1-4615-7819-2
- Andrew M. Gleason, Projective topological spaces, Illinois J. Math. 2 (1958), 482β489. MR 121775
- Norman Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36β41. MR 166752, DOI 10.2307/2312781
- J. Mioduszewski and L. Rudolf, $H$-closed and extremally disconnected Hausdorff spaces, Dissertationes Math. (Rozprawy Mat.) 66 (1969), 55. MR 256353
- Jack Porter and John Thomas, On $H$-closed and minimal Hausdorff spaces, Trans. Amer. Math. Soc. 138 (1969), 159β170. MR 238268, DOI 10.1090/S0002-9947-1969-0238268-4
- Travis Thompson, $S$-closed spaces, Proc. Amer. Math. Soc. 60 (1976), 335β338 (1977). MR 425899, DOI 10.1090/S0002-9939-1976-0425899-0
- Eric K. van Douwen, Existence and applications of remote points, Bull. Amer. Math. Soc. 84 (1978), no.Β 1, 161β163. MR 461463, DOI 10.1090/S0002-9904-1978-14454-1
- N. V. VeliΔko, $H$-closed topological spaces, Mat. Sb. (N.S.) 70 (112) (1966), 98β112 (Russian). MR 0198418
- Giovanni Viglino, $C$-compact spaces, Duke Math. J. 36 (1969), 761β764. MR 248749
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 687-692
- MSC: Primary 54D25; Secondary 54C10
- DOI: https://doi.org/10.1090/S0002-9939-1980-0587956-9
- MathSciNet review: 587956