{
  "id": "math/9907090",
  "version": "v7",
  "published": "1999-07-14T03:11:37.000Z",
  "updated": "1999-09-27T20:18:27.000Z",
  "title": "On the minimal cardinality of a subset of R which is not of first category",
  "authors": [
    "Apoloniusz Tyszka"
  ],
  "comment": "7 pages, added text about conditions C_m, to appear in J. Nat. Geom",
  "journal": "Journal of Natural Geometry 17 (2000), pp.21-28",
  "categories": [
    "math.LO"
  ],
  "abstract": "Let M be the ideal of first category subsets of R and non(M)=min{card X: X \\subseteq R, X \\not\\in M}. We consider families \\Phi of sequences converging to \\infty, with the property that for every open set U \\subseteq R that is unbounded above there exists a sequence belonging to \\Phi, which has an infinite number of terms belonging to U. We present assumptions about \\Phi which imply that the minimal cardinality of \\Phi equals non(M).",
  "revisions": [
    {
      "version": "v7",
      "updated": "1999-09-27T20:18:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05",
      "26A03"
    ],
    "keywords": [
      "minimal cardinality",
      "first category subsets",
      "open set",
      "infinite number",
      "equals non"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......7090T"
    }
  }
}