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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on spaces in which every open set is $z$-embedded
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by José L. Blasco PDF
Proc. Amer. Math. Soc. 85 (1982), 444-446 Request permission

Abstract:

Let $Oz$ be the class of topological spaces in which every open set is $z$-embedded. In this note we prove the following: If $Y$ is a dense subspace of the real line, then the spaces $\beta Y$ and $\beta Y - Y$ are not in $Oz$.
References
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  • Robert L. Blair, Čech-Stone remainders of locally compact nonpseudocompact spaces, Topology Proc. 4 (1979), no. 1, 13–17 (1980). MR 583685
  • 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
  • E. K. van Douwen, The Čech-Stone remainder of some nowhere locally compact spaces, manuscript.
  • 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
  • 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
  • © Copyright 1982 American Mathematical Society
  • 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