{
  "id": "2212.07077",
  "version": "v1",
  "published": "2022-12-14T07:56:13.000Z",
  "updated": "2022-12-14T07:56:13.000Z",
  "title": "The hyperspace of non-blockers of singletons, all the possible examples",
  "authors": [
    "Alejandro Illanes",
    "Benjamin Vejnar"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "Given a metric continuum $X$, a nonempty proper closed subspace $B$ of $X$, does not block a point $p\\in X\\setminus B$ provided that the union of all subcontinua of $X$ containing $p$ and contained in $X\\setminus B$ is a dense subset of $X$. The collection of all nonempty proper closed subspaces $B$ of $X$ such that $B$ does not block any element of $X\\setminus B$ is denoted by $NB(F_{1}(X))$. In this paper we prove that for each completely metrizable and separable space $Z$, there exists a continuum $X$ such that $Z$ is homeomorphic to $NB(F_{1}(X))$. This answers a series of questions by Camargo, Capul\\'in, Casta\\=neda-Alvarado and Maya.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-14T07:56:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54B20",
      "54F15"
    ],
    "keywords": [
      "nonempty proper closed subspace",
      "non-blockers",
      "hyperspace",
      "singletons",
      "metric continuum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}