{
  "id": "2002.07423",
  "version": "v1",
  "published": "2020-02-18T08:09:15.000Z",
  "updated": "2020-02-18T08:09:15.000Z",
  "title": "A countable dense homogeneous topological vector space is a Baire space",
  "authors": [
    "Tadeusz Dobrowolski",
    "Mikołaj Krupski",
    "Witold Marciszewski"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We prove that every homogeneous countable dense homogeneous topological space containing a copy of the Cantor set is a Baire space. In particular, every countable dense homogeneous topological vector space is a Baire space. It follows that, for any nondiscrete metrizable space $X$, the function space $C_p(X)$ is not countable dense homogeneous. This answers a question posed recently by R. Hern\\'andez-Guti\\'errez. We also conclude that, for any infinite dimensional Banach space $E$ (dual Banach space $E^\\ast$), the space $E$ equipped with the weak topology ($E^\\ast$ with the weak$^\\ast$ topology) is not countable dense homogeneous.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-18T08:09:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C35",
      "54E52",
      "46A03",
      "22A05"
    ],
    "keywords": [
      "dense homogeneous topological vector space",
      "countable dense homogeneous topological vector",
      "baire space",
      "dense homogeneous topological space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}