{
  "id": "1307.0184",
  "version": "v3",
  "published": "2013-06-30T07:31:20.000Z",
  "updated": "2014-06-10T18:25:32.000Z",
  "title": "Products and countable dense homogeneity",
  "authors": [
    "Andrea Medini"
  ],
  "comment": "7 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "Building on work of Baldwin and Beaudoin, assuming Martin's Axiom, we construct a zero-dimensional separable metrizable space $X$ such that $X$ is countable dense homogeneous while $X^2$ is not. It follows from results of Hru\\v{s}\\'ak and Zamora Avil\\'es that such a space $X$ cannot be Borel. Furthermore, $X$ can be made homogeneous and completely Baire as well.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-06-10T18:25:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54G20",
      "03E50",
      "54H05"
    ],
    "keywords": [
      "countable dense homogeneity",
      "zamora aviles",
      "zero-dimensional separable metrizable space",
      "assuming martins axiom"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.0184M"
    }
  }
}