Intersection of topologies and metrizability in topological groups (Q919111)

Generalizing a known result of \textit{P. J. Nyikos} [Proc. Am. Math. Soc. 83, 793-801 (1981; Zbl 0474.22001)] the author proves that in weakly- first-countable (in the sense of \textit{R. Sirois-Dumais} [Topology Appl. 11, 223-230 (1980; Zbl 0431.54015)]) topological groups the Fréchet- Urysohn property implies metrizability. As a corollary the following result is obtained: if a topological group (G,\(\tau\)) has the Fréchet- Urysohn property and \(\tau\) is a countable intersection of metrizable topologies, then \(\tau\) is metrizable.