{
  "id": "math/0311015",
  "version": "v1",
  "published": "2003-11-03T03:28:15.000Z",
  "updated": "2003-11-03T03:28:15.000Z",
  "title": "A compact group which is not Valdivia compact",
  "authors": [
    "Wieslaw Kubiś",
    "Vladimir Uspenskij"
  ],
  "comment": "4 pages",
  "journal": "Proc. Amer. Math. Soc. 133 (2005), 2483--2487",
  "doi": "10.1090/S0002-9939-05-07797-X",
  "categories": [
    "math.GN"
  ],
  "abstract": "A compact space $K$ is {\\em Valdivia compact} if it can be embedded in a Tikhonov cube $I^A$ in such a way that the intersection $K\\cap\\Sigma$ is dense in $K$, where $\\Sigma$ is the sigma-product (= the set of points with countably many non-zero coordinates). We show that there exists a compact connected Abelian group of weight $\\o_1$ which is not Valdivia compact, and deduce that Valdivia compact spaces are not preserved by open maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-03T03:28:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D30",
      "54C15",
      "22C05"
    ],
    "keywords": [
      "compact group",
      "compact connected abelian group",
      "valdivia compact spaces",
      "non-zero coordinates",
      "tikhonov cube"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11015K"
    }
  }
}