Discrete sets of singular cardinality
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- by William G. Fleissner PDF
- Proc. Amer. Math. Soc. 88 (1983), 743-745 Request permission
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
- William Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294–298. MR 362240, DOI 10.1090/S0002-9939-1974-0362240-4 W. S. Watson, Applications of set theory to topology, Ph.D. thesis, Univ. of Toronto, 1982.
Additional Information
- © Copyright 1983 American Mathematical Society
- 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