{
  "id": "0902.1944",
  "version": "v2",
  "published": "2009-02-11T17:06:30.000Z",
  "updated": "2009-09-02T18:57:34.000Z",
  "title": "Lindelof indestructibility, topological games and selection principles",
  "authors": [
    "Marion Scheepers",
    "Franklin D. Tall"
  ],
  "comment": "44 pages, 1 figure",
  "categories": [
    "math.GN",
    "math.LO"
  ],
  "abstract": "Arhangel'skii proved that if a first countable Hausdorff space is Lindel\\\"of, then its cardinality is at most $2^{\\aleph_0}$. Such a clean upper bound for Lindel\\\"of spaces in the larger class of spaces whose points are ${\\sf G}_{\\delta}$ has been more elusive. In this paper we continue the agenda started in F.D. Tall, On the cardinality of Lindel\\\"of spaces with points $G_{\\delta}$, Topology and its Applications 63 (1995), 21 - 38, of considering the cardinality problem for spaces satisfying stronger versions of the Lindel\\\"of property. Infinite games and selection principles, especially the Rothberger property, are essential tools in our investigations",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-09-02T18:57:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D20",
      "03E35",
      "03E55",
      "91A44"
    ],
    "keywords": [
      "selection principles",
      "lindelof indestructibility",
      "topological games",
      "first countable hausdorff space",
      "cardinality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.1944S"
    }
  }
}