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Metrizability And The Frechet-Urysohn Property In Topological Groups, Peter J. Nyikos

Faculty Publications

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 Fr&chet-Urysohn. A general necessary and sufficient condition for a sequential group to be Frechet-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".