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Metrizability and the Fréchet-Urysohn property in topological groups


Author: Peter J. Nyikos
Journal: Proc. Amer. Math. Soc. 83 (1981), 793-801
MSC: Primary 54E35
DOI: https://doi.org/10.1090/S0002-9939-1981-0630057-2
MathSciNet review: 630057
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Abstract: A question of Arhangel'skii, whether weakly first countable topological groups are metrizable, is answered in two ways: if the Hausdorff axiom is assumed, the answer is yes, but in general a weakly first countable topological group need not be pseudometrizable. The former result is obtained as a corollary of a more general sufficient condition for a sequential group to be Fréchet-Urysohn. A general necessary and sufficient condition for a sequential group to be Fréchet-Urysohn is given, and a number of questions are raised. Examples are given to show in what respect the theorems of the paper are the "best possible".


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DOI: https://doi.org/10.1090/S0002-9939-1981-0630057-2
Keywords: Topological group, weakly first countable, first countable, (pseudo-)symmetrizable, sequential, Fréchet-Urysohn
Article copyright: © Copyright 1981 American Mathematical Society

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