{
  "id": "1112.6374",
  "version": "v1",
  "published": "2011-12-29T18:48:37.000Z",
  "updated": "2011-12-29T18:48:37.000Z",
  "title": "Recognizing the topology of the space of closed convex subsets of a Banach space",
  "authors": [
    "Taras Banakh",
    "Ivan Hetman",
    "Katsuro Sakai"
  ],
  "comment": "10 pages",
  "categories": [
    "math.GT",
    "math.FA",
    "math.GN"
  ],
  "abstract": "Let $X$ be a Banach space and $Conv_H(X)$ be the space of non-empty closed convex subsets of $X$, endowed with the Hausdorff metric $d_H$. We prove that each connected component of the space $Conv_H(X)$ is homeomorphic to one of the spaces: a singleton, the real line, a closed half-plane, the Hilbert cube multiplied by the half-line, the separable Hilbert space, or a Hilbert space of density not less than continuum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-29T18:48:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N20",
      "46A55",
      "46B26",
      "46B20",
      "52B05",
      "03E65"
    ],
    "keywords": [
      "banach space",
      "non-empty closed convex subsets",
      "hausdorff metric",
      "real line",
      "hilbert cube"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.6374B"
    }
  }
}