A note on spaces in which every open set is -embedded
Author:
José L. Blasco
Journal:
Proc. Amer. Math. Soc. 85 (1982), 444-446
MSC:
Primary 54C50; Secondary 54C45, 54D40, 54G20
DOI:
https://doi.org/10.1090/S0002-9939-1982-0656120-9
MathSciNet review:
656120
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be the class of topological spaces in which every open set is
-embedded. In this note we prove the following: If
is a dense subspace of the real line, then the spaces
and
are not in
.
- [1] Robert L. Blair, Spaces in which special sets are 𝑧-embedded, Canadian J. Math. 28 (1976), no. 4, 673–690. MR 420542, https://doi.org/10.4153/CJM-1976-068-9
- [2] Robert L. Blair, Čech-Stone remainders of locally compact nonpseudocompact spaces, Topology Proc. 4 (1979), no. 1, 13–17 (1980). MR 583685
- [3] Robert L. Blair and Anthony W. Hager, Notes on the Hewitt realcompactification of a product, General Topology and Appl. 5 (1975), 1–8. MR 365496
- [4] E. K. van Douwen, The Čech-Stone remainder of some nowhere locally compact spaces, manuscript.
- [5] 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
- [6] Toshiji Terada, On spaces whose Stone-Čech compactification is Oz, Pacific J. Math. 85 (1979), no. 1, 231–237. MR 571637
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1982-0656120-9
Keywords:
-closure,
,
-embedding
Article copyright:
© Copyright 1982
American Mathematical Society