{
  "id": "1011.4555",
  "version": "v1",
  "published": "2010-11-20T06:38:34.000Z",
  "updated": "2010-11-20T06:38:34.000Z",
  "title": "Topological classification of zero-dimensional $M_ω$-groups",
  "authors": [
    "Taras Banakh"
  ],
  "comment": "4 pages",
  "journal": "Mat. Stud. 15:1 (2001) 109-112",
  "categories": [
    "math.GN",
    "math.GR"
  ],
  "abstract": "A topological group $G$ is called an $M_\\omega$-group if it admits a countable cover $\\K$ by closed metrizable subspaces of $G$ such that a subset $U$ of $G$ is open in $G$ if and only if $U\\cap K$ is open in $K$ for every $K\\in\\K$. It is shown that any two non-metrizable uncountable separable zero-dimenisional $M_\\omega$-groups are homeomorphic. Together with Zelenyuk's classification of countable $k_\\omega$-groups this implies that the topology of a non-metrizable zero-dimensional $M_\\omega$-group $G$ is completely determined by its density and the compact scatteredness rank $r(G)$ which, by definition, is equal to the least upper bound of scatteredness indices of scattered compact subspaces of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-20T06:38:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H11",
      "22A05",
      "54G12",
      "54F45"
    ],
    "keywords": [
      "topological classification",
      "compact scatteredness rank",
      "scatteredness indices",
      "upper bound",
      "scattered compact subspaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.4555B"
    }
  }
}