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Proceedings of the American Mathematical Society

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

 

 

Topological characterizations of pseudo-$ \aleph $-compact spaces


Author: Giovanni Vidossich
Journal: Proc. Amer. Math. Soc. 27 (1971), 195-198
MSC: Primary 54.52
DOI: https://doi.org/10.1090/S0002-9939-1971-0267532-2
MathSciNet review: 0267532
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Abstract: Pseudo-$ \aleph $-compact spaces, usually defined by cardinal bounds on uniform coverings of the fine uniformity, are characterized by cardinal bounds on locally finite open (resp. closed) coverings. This yields a new characterization of pseudo-compact spaces as well as of G. Aquaro's paralindelöfian spaces.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0267532-2
Keywords: Pseudo-$ \aleph $-compact space, pseudocompact space, paralindelöfian space, locally finite open (resp. closed) covering, Hilbert space $ {l_2}(\mathcal{U})$, one-point compactification, one-point pseudo-$ \aleph $-compactification, products
Article copyright: © Copyright 1971 American Mathematical Society