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Proceedings of the American Mathematical Society

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

 
 

 

The spaces which contain an $S$-space


Author: W. F. Pfeffer
Journal: Proc. Amer. Math. Soc. 85 (1982), 659-660
MSC: Primary 54A25; Secondary 28A05, 54H05
DOI: https://doi.org/10.1090/S0002-9939-1982-0660624-2
MathSciNet review: 660624
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Abstract: Under the continuum hypothesis, we show that a ${T_1}$-space $X$ contains an $S$-space if and only if there is an uncountable locally countable set $E \subset X$ containing no Borel subset of $X$.


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Keywords: Separable, Lindelöf, locally countable, Borel set, continuum hypothesis, Martin’s axiom
Article copyright: © Copyright 1982 American Mathematical Society