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Proceedings of the American Mathematical Society

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

 

 

The number of compact subsets of a topological space


Authors: D. K. Burke and R. E. Hodel
Journal: Proc. Amer. Math. Soc. 58 (1976), 363-368
MSC: Primary 54A25; Secondary 54D30
MathSciNet review: 0418014
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Abstract: Results are obtained which give an upper bound on the number of compact subsets of a topological space in terms of other cardinal invariants. The countable version of the main theorem states that an $ {\aleph _1}$-compact space with a point-countable separating open cover has at most $ {2^{{\aleph _0}}}$ compact subsets.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0418014-0
Keywords: Number of compact sets, density, Lindelöf degree, cellularity, $ {\aleph _1}$-compact, point-countable separating open cover
Article copyright: © Copyright 1976 American Mathematical Society