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A note on spaces in which every open set is $ z$-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: 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$.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0656120-9
Keywords: $ {G_\delta }$-closure, $ Oz$, $ z$-embedding
Article copyright: © Copyright 1982 American Mathematical Society

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