{
  "id": "1203.5824",
  "version": "v1",
  "published": "2012-03-26T21:38:30.000Z",
  "updated": "2012-03-26T21:38:30.000Z",
  "title": "On the cardinality of the $θ$-closed hull of sets",
  "authors": [
    "Filippo Cammaroto",
    "Andrei Catalioto",
    "Bruno Antonio Pansera",
    "Boaz Tsaban"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.GN"
  ],
  "abstract": "The \\theta-closed hull of a set A in a topological space is the smallest set C containing A such that, whenever all $closed$ neighborhoods of a point intersect C, this point is in C. We define a new topological cardinal invariant function, the $\\theta-bitighness small number$ of a space X, bts_theta(X), and prove that in every topological space X, the cardinality of the theta-closed hull of each set A is at most |A|^{bts_theta(X)}. Using this result, we synthesize all earlier results on bounds on the cardinality of theta-closed hulls. We provide applications to P-spaces and to the almost-Lindelof number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-03-26T21:38:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cardinality",
      "topological cardinal invariant function",
      "theta-closed hull",
      "topological space",
      "smallest set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.5824C"
    }
  }
}