{
  "id": "1302.5658",
  "version": "v3",
  "published": "2013-02-22T17:42:09.000Z",
  "updated": "2014-09-13T07:25:17.000Z",
  "title": "Topologically invariant $σ$-ideals on the Hilbert cube",
  "authors": [
    "Taras Banakh",
    "Michal Morayne",
    "Robert Ralowski",
    "Szymon Zeberski"
  ],
  "comment": "14 pages",
  "categories": [
    "math.GT",
    "math.GN",
    "math.LO"
  ],
  "abstract": "We study and classify topologically invariant $\\sigma$-ideals with a Borel base on the Hilbert cube and evaluate their cardinal characteristics. One of the results of this paper solves (positively) a known problem whether the minimal cardinalities of the families of Cantor sets covering the unit interval and the Hilbert cube are the same.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-02-27T19:17:48.000Z",
      "comment": "16 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-09-13T07:25:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "03E17",
      "54H05",
      "55M10",
      "57N20"
    ],
    "keywords": [
      "hilbert cube",
      "cardinal characteristics",
      "unit interval",
      "minimal cardinalities",
      "cantor sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.5658B"
    }
  }
}