Fréchet-Urysohn fans in free topological groups
arXiv:0803.4117 · doi:10.1016/j.jpaa.2007.12.006
Abstract
In this paper we answer the question of T. Banakh and M. Zarichnyi constructing a copy of the Fréchet-Urysohn fan $S_\w$ in a topological group admitting a functorial embedding . The latter means that each autohomeomorphism of extends to a continuous homomorphism of . 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 containing a topological copy of the space $\IQ$ of rationals give topological groups containing $S_\w$.