Fréchet-Urysohn fans in free topological groups

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dc.creatorBanakh, Taras
dc.creatorRepovš, Dušan
dc.creatorZdomskyy, Lyubomyr
dc.date2008-03-28
dc.date.accessioned2026-07-07T09:40:30Z
dc.date.available2026-07-07T09:40:30Z
dc.descriptionIn 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 $G$ 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 $S_\w$.
dc.identifierhttps://arxiv.org/abs/0803.4117
dc.identifierhttp://arxiv.org/abs/0803.4117
dc.identifierJ. Pure Appl. Algebra 212:9 (2008), 2105-2114.
dc.identifierdoi:10.1016/j.jpaa.2007.12.006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161504
dc.subjectGeneral Topology
dc.subject18B30; 22A05; 54C20; 54E35; 54F15
dc.titleFréchet-Urysohn fans in free topological groups
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