{
  "id": "math/9912056",
  "version": "v4",
  "published": "1999-12-07T22:48:38.000Z",
  "updated": "2000-01-28T02:28:32.000Z",
  "title": "A combinatorial characterization of second category subsets of X^ω",
  "authors": [
    "Apoloniusz Tyszka"
  ],
  "comment": "with a counterexample by T. Bartoszynski, to appear in J. Nat. Geom",
  "journal": "Journal of Natural Geometry 18 (2000), pp.125-130",
  "categories": [
    "math.LO",
    "math-ph",
    "math.GN",
    "math.MP"
  ],
  "abstract": "Let a finite non-empty X is equipped with discrete topology. We prove that S \\subseteq X^\\omega is of second category if and only if for each f:\\omega -> \\bigcup_{n \\in \\omega} X^n there exists a sequence {a_n}_{n \\in \\omega} belonging to S such that for infinitely many i \\in \\omega the infinite sequence {a_{i+n}}_{n \\in \\omega} extends the finite sequence f(i).",
  "revisions": [
    {
      "version": "v4",
      "updated": "2000-01-28T02:28:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05",
      "54E52"
    ],
    "keywords": [
      "second category subsets",
      "combinatorial characterization",
      "infinite sequence",
      "discrete topology"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....12056T"
    }
  }
}