{
  "id": "1107.1435",
  "version": "v2",
  "published": "2011-07-07T15:57:18.000Z",
  "updated": "2011-10-22T22:01:33.000Z",
  "title": "For Hausdorff spaces, $H$-closed = $D$-pseudocompact for all ultrafilters $D$",
  "authors": [
    "Paolo Lipparini"
  ],
  "comment": "v. 2: added some results, some remarks, various minor improvements. 7 pages. v. 1: 4 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "We prove that, for an arbitrary topological space $X$, the following two conditions are equivalent: (a) Every open cover of $X$ has a finite subset with dense union (b) $X$ is $D$-pseudocompact, for every ultrafilter $D$. Locally, our result asserts that if $X$ is weakly initially $\\lambda$-compact, and $2^ \\mu \\leq \\lambda $, then $X$ is $D$-\\brfrt pseudocompact, for every ultrafilter $D$ over any set of cardinality $ \\leq \\mu$. As a consequence, if $2^ \\mu \\leq \\lambda $, then the product of any family of weakly initially $\\lambda$-compact spaces is weakly initially $\\mu$-compact.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-22T22:01:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D20",
      "54B10",
      "54A20"
    ],
    "keywords": [
      "hausdorff spaces",
      "pseudocompact",
      "ultrafilter",
      "result asserts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.1435L"
    }
  }
}