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Proceedings of the American Mathematical Society

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

 
 

 

Nonperfect spaces with point-countable bases


Author: Peter Davies
Journal: Proc. Amer. Math. Soc. 77 (1979), 276-278
MSC: Primary 54E99; Secondary 03E35, 54G20
DOI: https://doi.org/10.1090/S0002-9939-1979-0542097-3
MathSciNet review: 542097
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Abstract: We construct a completely regular space of cardinality $ {\aleph _1}$ with a point-countable base, which is not perfect. This answers a question of Fleissner and Reed. We also construct, under the hypothesis $ {2^{{\aleph _0}}} < {2^{{\aleph _1}}}$, a hereditarily normal space of cardinality $ {\aleph _1}$ with a $ \sigma $-disjoint base, which is not perfect.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0542097-3
Keywords: Point-countable base, perfect
Article copyright: © Copyright 1979 American Mathematical Society

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