Fréchet-Urysohn fans in free topological groups

Details Fréchet-Urysohn fans in free topological groups Fréchet-Urysohn fans in free topological groups

2008-03-28

arxiv.org/abs/0803.4117v1

J. Pure Appl. Algebra 212:9 (2008), 2105-2114.

Mathematics

General Topology

Scientific paper

10.1016/j.jpaa.2007.12.006

In this paper we answer the question of T. Banakh and M. Zarichnyi constructing a copy of the Fr\'echet-Urysohn fan $S_\w$ in a topological group $G$ admitting a functorial embedding $[0,1]\subset G$. The latter means that each autohomeomorphism of $[0,1]$ extends to a continuous homomorphism of $G$. This implies that many natural free topological group constructions (e.g. the constructions of the Markov free topological group, free abelian topological group, free totally bounded group, free compact group) applied to a Tychonov space $X$ containing a topological copy of the space $\IQ$ of rationals give topological groups containing $S_\w$.

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