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Proceedings of the American Mathematical Society

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



Discrete sets of singular cardinality

Author: William G. Fleissner
Journal: Proc. Amer. Math. Soc. 88 (1983), 743-745
MSC: Primary 54D15
MathSciNet review: 702311
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Abstract: Let $ \kappa $ be a singular cardinal. In Fleissner's thesis, he showed that in normal spaces $ X$, certain discrete sets $ Y$ of cardinality $ \kappa $ (called here sparse) which are $ < \kappa $-separated are, in fact, separated. In Watson's thesis, he proves the same for countably paracompact spaces $ X$. Here we improve these results by making no assumption on the space $ X$. As a corollary, we get that assuming $ V = L$, $ {\aleph _1}$,-paralindelöf $ {T_2}$, spaces of character $ \leqslant {\omega _2}$, are collectionwise Hausdorff.

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Keywords: Discrete, singular cardinals, collectionwise Hausdorff
Article copyright: © Copyright 1983 American Mathematical Society

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