{
  "id": "1808.09584",
  "version": "v1",
  "published": "2018-08-28T23:56:07.000Z",
  "updated": "2018-08-28T23:56:07.000Z",
  "title": "The hyperspace of non blockers of $F_1(X)$",
  "authors": [
    "Javier Camargo",
    "David Maya",
    "Luis Ortiz"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "A continuum is a compact connected metric space. A non-empty closed subset $B$ of a continuum $X$ does not block $x\\in X\\setminus B$ provided that the union of all subcontinua of $X$ containing $x$ and contained in $X\\setminus B$ is dense in $X$. We denote the collection of all non-empty closed subset $B$ of $X$ such that $B$ does not block each element of $X\\setminus B$ by $NB(F_1(X))$. In this paper we show some properties of the hyperspace $NB(F_1(X))$. Particularly, we prove that the simple closed curve is the unique continuum $X$ such that $NB(F_1(X))=F_1(X)$, given a positive answer to a question posed by Escobedo, Estrada-Obreg\\'on and Villanueva in 2012.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-28T23:56:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54B20",
      "54F15"
    ],
    "keywords": [
      "non blockers",
      "hyperspace",
      "non-empty closed subset",
      "compact connected metric space",
      "unique continuum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}