{
  "id": "1306.5463",
  "version": "v2",
  "published": "2013-06-23T19:42:29.000Z",
  "updated": "2013-06-27T13:26:49.000Z",
  "title": "Topological games and Alster spaces",
  "authors": [
    "Leandro F. Aurichi",
    "Rodrigo R. Dias"
  ],
  "comment": "13 pages; submitted",
  "categories": [
    "math.GN"
  ],
  "abstract": "In this paper we study connections between topological games such as Rothberger, Menger and compact-open, and relate these games to properties involving covers by G_{\\delta} subsets. The results include: (1) If Two has a winning strategy in the Menger game on a regular space X, then X is an Alster space. (2) If Two has a winning strategy in the Rothberger game on a topological space X, then the G_\\delta-topology on X is Lindelof. (3) The Menger game and the compact-open game are (consistently) not dual.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-27T13:26:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D20",
      "54G99",
      "54A10"
    ],
    "keywords": [
      "alster space",
      "topological games",
      "menger game",
      "winning strategy",
      "study connections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.5463A"
    }
  }
}