{
  "id": "math/0309101",
  "version": "v1",
  "published": "2003-09-05T16:38:18.000Z",
  "updated": "2003-09-05T16:38:18.000Z",
  "title": "The Urysohn universal metric space is homeomorphic to a Hilbert space",
  "authors": [
    "Vladimir Uspenskij"
  ],
  "comment": "5 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "The Urysohn universal metric space U is characterized up to isometry by the following properties: (1) U is complete and separable; (2) U contains an isometric copy of every separable metric space; (3) every isometry between two finite subsets of U can be extended to an isometry of U onto itself. We show that U is homeomorphic to the Hilbert space l_2 (or to the countable power of the real line).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-09-05T16:38:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54F65",
      "54C55",
      "54D70",
      "54E35",
      "54E50"
    ],
    "keywords": [
      "urysohn universal metric space",
      "hilbert space",
      "homeomorphic",
      "isometric copy",
      "separable metric space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......9101U"
    }
  }
}