{
  "id": "1212.5724",
  "version": "v2",
  "published": "2012-12-22T20:57:41.000Z",
  "updated": "2013-02-21T11:08:44.000Z",
  "title": "Infinite games and cardinal properties of topological spaces",
  "authors": [
    "Angelo Bella",
    "Santi Spadaro"
  ],
  "comment": "Corrected an error in the proof of Theorem 3.6",
  "categories": [
    "math.GN"
  ],
  "abstract": "Inspired by work of Scheepers and Tall, we use properties defined by topological games to provide bounds for the cardinality of topological spaces. We obtain a partial answer to an old question of Bell, Ginsburg and Woods regarding the cardinality of weakly Lindel\\\"of first-countable regular spaces and answer a question recently asked by Babinkostova, Pansera and Scheepers. In the second part of the paper we study a game-theoretic version of cellularity, a special case of which has been introduced by Aurichi. We obtain a game-theoretic proof of Shapirovskii's bound for the number of regular open sets in an (almost) regular space and give a partial answer to a natural question about the productivity of a game strengthening of the countable chain condition that was introduced by Aurichi. As a final application of our results we prove that the Hajnal-Juh\\'asz bound for the cardinality of a first-countable ccc Hausdorff space is true for almost regular (non-Hausdorff) spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-02-21T11:08:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A25",
      "91A44",
      "54D35",
      "54D10"
    ],
    "keywords": [
      "topological spaces",
      "infinite games",
      "cardinal properties",
      "partial answer",
      "first-countable ccc hausdorff space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.5724B"
    }
  }
}