{
  "id": "1605.05630",
  "version": "v1",
  "published": "2016-05-18T15:51:36.000Z",
  "updated": "2016-05-18T15:51:36.000Z",
  "title": "$G_δ$ covers of compact spaces",
  "authors": [
    "Santi Spadaro",
    "Paul Szeptycki"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We prove that in a countably compact weakly Lindelof normal space of countable tightness, every $G_\\delta$ cover has a continuum-sized subcollection with a $G_\\delta$-dense union and that in a Lindelof space with a base of multiplicity continuum, every $G_\\delta$ cover has a continuum sized subcover. We also solve a long standing question due to Arhangel'skii by constructing a compact space which has a $G_\\delta$ cover with no continuum-sized ($G_\\delta$)-dense subcollection.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-18T15:51:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact space",
      "compact weakly lindelof normal space",
      "countably compact weakly lindelof normal",
      "long standing question",
      "dense subcollection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}