{
  "id": "2211.07972",
  "version": "v1",
  "published": "2022-11-15T08:19:34.000Z",
  "updated": "2022-11-15T08:19:34.000Z",
  "title": "A Hofmann-Mislove theorem for $c$-well-filtered spaces",
  "authors": [
    "Liping Zhang",
    "Xiangnan Zhou",
    "Qingguo Li"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "The Hofmann-Mislove theorem states that in a sober space, the nonempty Scott open filters of its open set lattice correspond bijectively to its compacts saturated sets. In this paper, the concept of $c$-well-filtered spaces is introduced. We show that a retract of a $c$-well-filtered space is $c$-well-filtered and a locally Lindel\\\"{o}f and $c$-well-filtered $P$-space is countably sober. In particular, we obtain a Hofmann-Mislove theorem for $c$-well-filtered spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-15T08:19:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H99"
    ],
    "keywords": [
      "well-filtered space",
      "nonempty scott open filters",
      "open set lattice correspond",
      "hofmann-mislove theorem states",
      "sober space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}