{
  "id": "1809.06816",
  "version": "v1",
  "published": "2018-09-18T16:24:43.000Z",
  "updated": "2018-09-18T16:24:43.000Z",
  "title": "Countable Dense Homogeneity and the Double Arrow Space",
  "authors": [
    "Rodrigo Hernández-Gutiérrez"
  ],
  "journal": "Top. Applications 160, 10, (2013), 1123-1128",
  "categories": [
    "math.GN"
  ],
  "abstract": "Let $\\mathbb{A}$ denote the Alexandroff-Urysohn double arrow space. We prove the following results: (a) $\\mathbb{A}\\times{}^\\omega{2}$ is not countable dense homogeneous; (b) ${}^{\\omega}{\\mathbb{A}}$ is not countable dense homogeneous; (c) $\\mathbb{A}$ has exactly $\\mathfrak{c}$ types of countable dense subsets. These results answer questions by Arhangel'ski\\u\\i, Hru\\v{s}\\'ak and van Mill.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-18T16:24:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54B10",
      "54D65",
      "54F05"
    ],
    "keywords": [
      "countable dense homogeneity",
      "alexandroff-urysohn double arrow space",
      "results answer questions",
      "countable dense homogeneous",
      "van mill"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}