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Proceedings of the American Mathematical Society

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

 

 

Another view of metrizability


Author: H. H. Hung
Journal: Proc. Amer. Math. Soc. 101 (1987), 551-554
MSC: Primary 54E35
DOI: https://doi.org/10.1090/S0002-9939-1987-0908667-X
MathSciNet review: 908667
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Abstract: A fact long considered unsatisfactory about the classical metrization theorem of Alexandroff-Urysohn is that it expresses metrizability as a countable uniformity, uniformity itself being almost the former. In view of their unification, the classical theorems, with the exception of Arhangel'skiĭ's regular open base theorem, are all really subject to the same criticism, to which our theorem here is an answer. We give a generalization here of Arhangel'skiĭ's, of which Arhangel'skiĭ's itself, the fundamental theorem of Alexandroff-Urysohn, A. H. Frink's, and the Double Sequence Theorem of Nagata are all obvious special cases.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0908667-X
Keywords: Metrizability without uniformity among members of bases, pairnetworks, nests, companions of nests, capture of nests by their companions
Article copyright: © Copyright 1987 American Mathematical Society