{
  "id": "1705.01203",
  "version": "v1",
  "published": "2017-05-02T23:32:16.000Z",
  "updated": "2017-05-02T23:32:16.000Z",
  "title": "Countable dense homogeneity and the Cantor set",
  "authors": [
    "Rodrigo Hernández-Gutiérrez"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "It is shown that CH implies the existence of a compact Hausdorff space that is countable dense homogeneous, crowded and does not contain topological copies of the Cantor set. This contrasts with a previous result by the author which says that for any crowded Hausdorff space $X$ of countable $\\pi$-weight, if ${}^\\omega{X}$ is countable dense homogeneous, then $X$ must contain a topological copy of the Cantor set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-02T23:32:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54G20",
      "54D65",
      "54D30",
      "54B35"
    ],
    "keywords": [
      "cantor set",
      "countable dense homogeneity",
      "topological copy",
      "compact hausdorff space",
      "countable dense homogeneous"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}