{
  "id": "0911.1023",
  "version": "v2",
  "published": "2009-11-05T20:48:36.000Z",
  "updated": "2011-12-04T04:09:58.000Z",
  "title": "Products and h-homogeneity",
  "authors": [
    "Andrea Medini"
  ],
  "comment": "10 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "Building on work of Terada, we prove that h-homogeneity is productive in the class of zero-dimensional spaces. Then, by generalizing a result of Motorov, we show that for every non-empty zero-dimensional space $X$ there exists a non-empty zero-dimensional space $Y$ such that $X\\times Y$ is h-homogeneous. Also, we simultaneously generalize results of Motorov and Terada by showing that if $X$ is a space such that the isolated points are dense then $X^\\kappa$ is h-homogeneous for every infinite cardinal $\\kappa$. Finally, we show that a question of Terada (whether $X^\\omega$ is h-homogeneous for every zero-dimensional first-countable $X$) is equivalent to a question of Motorov (whether such an infinite power is always divisible by 2) and give some partial answers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-04T04:09:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54B10"
    ],
    "keywords": [
      "non-empty zero-dimensional space",
      "h-homogeneity",
      "infinite cardinal",
      "infinite power",
      "partial answers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.1023M"
    }
  }
}