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Discrete sets of singular cardinality


Author: William G. Fleissner
Journal: Proc. Amer. Math. Soc. 88 (1983), 743-745
MSC: Primary 54D15
DOI: https://doi.org/10.1090/S0002-9939-1983-0702311-9
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.


References [Enhancements On Off] (What's this?)

  • [F] W. G. Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294-298. MR 0362240 (50:14682)
  • [W] W. S. Watson, Applications of set theory to topology, Ph.D. thesis, Univ. of Toronto, 1982.

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DOI: https://doi.org/10.1090/S0002-9939-1983-0702311-9
Keywords: Discrete, singular cardinals, collectionwise Hausdorff
Article copyright: © Copyright 1983 American Mathematical Society

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