{
  "id": "1910.14483",
  "version": "v1",
  "published": "2019-10-31T14:20:29.000Z",
  "updated": "2019-10-31T14:20:29.000Z",
  "title": "On first countable, cellular-compact spaces",
  "authors": [
    "István Juhász",
    "Lajos Soukup",
    "Zoltán Szentmiklóssy"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "A topological space $X$ is cellular-compact if given any cellular family $\\mathcal U$ of open subsets of $X$ there is a compact subspace $K\\subset X$ such that $K\\cap U\\ne \\emptyset$ for each $U\\in \\mathcal U$. Answering two questions of Tkachuk and Wilson we show that (1) if $X$ is a first countable cellular-compact $T_2$ space, then $|X|\\le 2^{\\omega}$, (2) if $cov(\\mathcal M)>{\\omega}_1$, then every first countable separable $\\pi$-regular cellular-compact space is compact.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-31T14:20:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D20",
      "54D99",
      "54D55"
    ],
    "keywords": [
      "regular cellular-compact space",
      "compact subspace",
      "open subsets",
      "first countable cellular-compact",
      "topological space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}