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Proceedings of the American Mathematical Society

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

 
 

 

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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Keywords: <!– MATH ${G_\delta }$ –> <IMG WIDTH="30" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img5.gif" ALT="${G_\delta }$">-closure, <IMG WIDTH="32" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$Oz$">, <IMG WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$z$">-embedding
Article copyright: © Copyright 1982 American Mathematical Society