{
  "id": "1506.07666",
  "version": "v1",
  "published": "2015-06-25T08:50:25.000Z",
  "updated": "2015-06-25T08:50:25.000Z",
  "title": "Non-homeomorphic topological rank and expansiveness",
  "authors": [
    "Takashi Shimomura"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Downarowicz and Maass (2008) have shown that every Cantor minimal homeomorphism with finite topological rank $K > 1$ is expansive. Bezuglyi, Kwiatkowski and Medynets (2009) extended the result to non-minimal cases. On the other hand, Gambaudo and Martens (2006) had expressed all Cantor minimal continuou surjections as the inverse limit of graph coverings. In this paper, we define a topological rank for every Cantor minimal continuous surjection, and show that every Cantor minimal continuous surjection of finite topological rank has the natural extension that is expansive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-25T08:50:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "54H20"
    ],
    "keywords": [
      "non-homeomorphic topological rank",
      "cantor minimal continuous surjection",
      "finite topological rank",
      "expansiveness",
      "cantor minimal continuou surjections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150607666S"
    }
  }
}