{
  "id": "1912.03411",
  "version": "v1",
  "published": "2019-12-07T01:57:01.000Z",
  "updated": "2019-12-07T01:57:01.000Z",
  "title": "About the uniqueness of the hyperspaces $C(p,X)$ in some classes of continua",
  "authors": [
    "Florencio Corona-Vázquez",
    "Russell Aarón Quiñones-Estrella",
    "Javier Sánchez-Martínez"
  ],
  "comment": "12 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "Given a continuum $X$ and $p\\in X$, we will consider the hyperspace $C(p,X)$ of all subcontinua of $X$ containing $p$. Given a family of continua $\\mathcal{C}$, a continuum $X\\in\\mathcal{C}$ and $p\\in X$, we say that $(X,p)$ has unique hyperspace $C(p,X)$ relative to $\\mathcal{C}$ if for each $Y\\in\\mathcal{C}$ and $q\\in Y$ such that $C(p,X)$ and $C(q,Y)$ are homeomorphic, then there is an homeomorphism between $X$ and $Y$ sending $p$ to $q$. In this paper we show that $(X,p)$ has unique hyperspace $C(p,X)$ relative to the classes of dendrites if and only if $X$ is a tree, we present also some classes of continua without unique hyperspace $C(p,X)$; this answer some questions posed in \\cite{Corona.et.al(2019)}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-07T01:57:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unique hyperspace",
      "uniqueness",
      "subcontinua"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}