{
  "id": "1905.00564",
  "version": "v1",
  "published": "2019-05-02T03:30:25.000Z",
  "updated": "2019-05-02T03:30:25.000Z",
  "title": "Hyperspaces $C(p,X)$ of finite graphs",
  "authors": [
    "Florencio Corona-Vázquez",
    "Russell Aarón Quiñones Estrella",
    "Javier Sánchez-Martínez",
    "Hugo Villanueva"
  ],
  "comment": "16 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 $p$ and the family $K(X)$ of all hyperspaces $C(q,X)$, where $q\\in X$. In this paper we give some conditions on the points $p,q\\in X$ to guarantee that $C(p,X)$ and $C(q,X)$ are homeomorphic, for finite graphs $X$. Also, we study the relationship between the homogeneity degree of a finite graph $X$ and the number of topologically distinct spaces in $K(X)$, called the size of $K(X)$. In addition, we construct for each positive integer $n$, a finite graph $X_n$ such that $K(X_n)$ has size $n$, and we present a theorem that allows to construct finite graphs $X$ with a degree of homogeneity different from the size of the family $K(X)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-02T03:30:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54B20"
    ],
    "keywords": [
      "hyperspace",
      "construct finite graphs",
      "homogeneity degree",
      "topologically distinct spaces",
      "conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}