{
  "id": "math/0410507",
  "version": "v2",
  "published": "2004-10-23T10:50:03.000Z",
  "updated": "2004-10-27T14:07:15.000Z",
  "title": "Topologies on the group of homeomorphisms of a Cantor set",
  "authors": [
    "Sergey Bezuglyi",
    "Anthony H. Dooley",
    "Jan Kwiatkowski"
  ],
  "comment": "33 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $Homeo(\\Omega)$ be the group of all homeomorphisms of a Cantor set $\\Omega$. We study topological properties of $Homeo(\\Omega)$ and its subsets with respect to the uniform $(\\tau)$ and weak $(\\tau_w)$ topologies. The classes of odometers and periodic, aperiodic, minimal, rank 1 homeomorphisms are considered and the closures of those classes in $\\tau$ and $\\tau_w$ are found.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-10-27T14:07:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "37A40"
    ],
    "keywords": [
      "cantor set",
      "homeomorphisms",
      "topologies",
      "study topological properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10507B"
    }
  }
}