{
  "id": "0904.1389",
  "version": "v1",
  "published": "2009-04-08T17:35:23.000Z",
  "updated": "2009-04-08T17:35:23.000Z",
  "title": "o-Boundedness of free topological groups",
  "authors": [
    "Taras Banakh",
    "Dušan Repovš",
    "Lyubomyr Zdomskyy"
  ],
  "comment": "24 pages, submitted",
  "journal": "Topology and Its Applications 157:2 (2010), 466-481.",
  "doi": "10.1016/j.topol.2009.10.006",
  "categories": [
    "math.GN"
  ],
  "abstract": "Assuming the absence of Q-points (which is consistent with ZFC) we prove that the free topological group $F(X)$ over a Tychonov space $X$ is $o$-bounded if and only if every continuous metrizable image $T$ of $X$ satisfies the selection principle $U_{fin}(O,\\Omega)$ (the latter means that for every sequence $<u_n>_{n\\in w}$ of open covers of $T$ there exists a sequence $<v_n>_{n\\in w}$ such that $v_n\\in [u_n]^{<w}$ and for every $F\\in [X]^{<w}$ there exists $n\\in w$ with $F\\subset\\cup v_n$). This characterization gives a consistent answer to a problem posed by C. Hernandes, D. Robbie, and M. Tkachenko in 2000.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-08T17:35:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H11",
      "54D20",
      "20N02",
      "57S05"
    ],
    "keywords": [
      "free topological group",
      "o-boundedness",
      "tychonov space",
      "selection principle",
      "open covers"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.1389B"
    }
  }
}