On topological groups containing a Fréchet-Urysohn fan

Details On topological groups containing a Fréchet-Urysohn fan On topological groups containing a Fréchet-Urysohn fan

2009-11-20

arxiv.org/abs/0911.4081v1

Mat. Stud. 9:2 (1998), 149--154

Mathematics

General Topology

Scientific paper

Suppose G is a topological group containing a (closed) topological copy of the Frechet-Urysohn fan. If G is a perfectly normal sequential space (a normal k-space) then every closed metrizable subset in $G$ is locally compact. Applying this result to topological groups whose underlying topological space can be written as a direct limit of a sequence of closed metrizable subsets, we get that every such a group either is metrizable or is homeomorphic to the product of a $k_\omega$-space and a discrete space.

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