Fréchet-Urysohn fans in free topological groups |
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Authors: | Taras Banakh Dušan Repovš Lyubomyr Zdomskyy |
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Institution: | a Instytut Matematyki, Akademia ?wi?tokrzyska 15, Kielce 25-406, Poland b Department of Mechanics and Mathematics, Ivan Franko Lviv National University, Universytetska 1, Lviv, 79000, Ukraine c Institute of Mathematics, Physics and Mechanics, University of Ljubljana, P.O.B. 2964, Ljubljana 1001, Slovenia |
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Abstract: | In this paper we answer the question of T. Banakh and M. Zarichnyi constructing a copy of the Fréchet-Urysohn fan Sω in a topological group G admitting a functorial embedding 0,1]⊂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 Q of rationals give topological groups containing Sω. |
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Keywords: | 18B30 22A05 54C20 54E35 54F15 |
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