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Proceedings of the American Mathematical Society

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A nonparacompact space which admits a closure-preserving cover of compact sets


Author: H. B. Potoczny
Journal: Proc. Amer. Math. Soc. 32 (1972), 309-311
MSC: Primary 54.50
DOI: https://doi.org/10.1090/S0002-9939-1972-0288727-9
MathSciNet review: 0288727
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Abstract: In [1], Tamano asked whether or not a space which is the union of a closure-preserving family of compact subsets must be paracompact. It is the purpose of this paper to present a space which admits such a cover, is completely regular and $ {T_2}$, has a basis consisting of open and closed sets, yet fails to be even normal.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0288727-9
Keywords: Compact, paracompact, metacompact, closure-preserving
Article copyright: © Copyright 1972 American Mathematical Society