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Maximal extensions of first-countable spaces


Authors: Toshiji Terada and Jun Terasawa
Journal: Proc. Amer. Math. Soc. 85 (1982), 95-99
MSC: Primary 54D20; Secondary 54C20
DOI: https://doi.org/10.1090/S0002-9939-1982-0647906-5
MathSciNet review: 647906
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Abstract: A first-countable space is called maximal if it is not contained as a dense subspace in a first-countable space properly. The following are shown; (1) every locally compact, first-countable space is a dense subspace of a maximal space, (2) every metrizable space is a dense subspace of a maximal space, and (3) there is a first-countable space which is not a dense subspace of any maximal space.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0647906-5
Keywords: First-countable, pseudocompact, maximal extension, locally compact, metrizable, Čech-complete
Article copyright: © Copyright 1982 American Mathematical Society

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