{
  "id": "math/0510032",
  "version": "v2",
  "published": "2005-10-03T07:34:45.000Z",
  "updated": "2007-01-24T07:36:52.000Z",
  "title": "On approximation of homeomorphisms of a Cantor set",
  "authors": [
    "Konstantin Medynets"
  ],
  "comment": "12 pages: typos fixed",
  "journal": "Fundamenta Mathematicae 194 (2007), p.1-13",
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "We continue to study topological properties of the group Homeo(X) of all homeomorphisms of a Cantor set X with respect to the uniform topology tau, which was started in the paper (S. Bezuglyi, A.H. Dooley, and J. Kwiatkowski, Topologies on the group of homeomorphisms of a Cantor set, ArXiv e-print math.DS/0410507, 2004). We prove that the set of periodic homeomorphisms is tau-dense in Homeo(X) and deduce from this result that the topological group (Homeo(X), tau) has the Rokhlin property, i.e., there exists a homeomorphism whose conjugate class is tau-dense in Homeo(X). We also show that for any homeomorphism T the topological full group [[T]] is tau-dense in the full group [T].",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-01-24T07:36:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "54H11"
    ],
    "keywords": [
      "cantor set",
      "approximation",
      "uniform topology tau",
      "e-print math",
      "group homeo"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10032M"
    }
  }
}