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Discrete subsets of perfectly normal spaces


Author: R. M. Stephenson
Journal: Proc. Amer. Math. Soc. 34 (1972), 605-608
MSC: Primary 54A25; Secondary 54B15
DOI: https://doi.org/10.1090/S0002-9939-1972-0296885-5
MathSciNet review: 0296885
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Abstract: Following R. W. Heath and E. A. Michael [HM], we call a topological space perfect if each of its closed subsets is a $ {G_\delta }$.

In this note we (i) give a characterization of compact perfect $ {T_1}$ spaces and (ii) obtain some results concerning the cardinality of discrete subsets of perfect spaces.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0296885-5
Keywords: Compact perfectly normal spaces, discrete subspaces, countably compact perfect spaces
Article copyright: © Copyright 1972 American Mathematical Society

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