{
  "id": "1811.00660",
  "version": "v1",
  "published": "2018-11-01T22:26:53.000Z",
  "updated": "2018-11-01T22:26:53.000Z",
  "title": "Cardinal invariants of cellular-Lindelof spaces",
  "authors": [
    "Angelo Bella",
    "Santi Spadaro"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "A space $X$ is said to be \"cellular-Lindel\\\"of\" if for every cellular family $\\mathcal{U}$ there is a Lindel\\\"of subspace $L$ of $X$ which meets every element of $\\mathcal{U}$. Cellular-Lindel\\\"of spaces generalize both Lindel\\\"of spaces and spaces with the countable chain condition. Solving questions of Xuan and Song, we prove that every cellular-Lindel\\\"of monotonically normal space is Lindel\\\"of and that every cellular-Lindel\\\"of space with a regular $G_\\delta$-diagonal has cardinality at most $2^\\mathfrak{c}$. We also prove that every normal cellular-Lindel\\\"of first-countable space has cardinality at most continuum under $2^{<\\mathfrak{c}}=\\mathfrak{c}$ and that every normal cellular Lindel\\\"of space with a $G_\\delta$-diagonal of rank $2$ has cardinality at most continuum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-01T22:26:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cardinal invariants",
      "cellular-lindelof spaces",
      "cardinality",
      "countable chain condition",
      "monotonically normal space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}