{
  "id": "0803.4117",
  "version": "v1",
  "published": "2008-03-28T15:58:42.000Z",
  "updated": "2008-03-28T15:58:42.000Z",
  "title": "Fréchet-Urysohn fans in free topological groups",
  "authors": [
    "Taras Banakh",
    "Dušan Repovš",
    "Lyubomyr Zdomskyy"
  ],
  "journal": "J. Pure Appl. Algebra 212:9 (2008), 2105-2114.",
  "doi": "10.1016/j.jpaa.2007.12.006",
  "categories": [
    "math.GN"
  ],
  "abstract": "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 $S_\\w$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-28T15:58:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18B30",
      "22A05",
      "54C20",
      "54E35",
      "54F15"
    ],
    "keywords": [
      "fréchet-urysohn fans",
      "natural free topological group constructions",
      "free abelian topological group",
      "markov free topological group",
      "free compact group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.4117B"
    }
  }
}