{
  "id": "0902.2258",
  "version": "v3",
  "published": "2009-02-13T04:42:09.000Z",
  "updated": "2010-05-04T11:54:12.000Z",
  "title": "Locally precompact groups: (Local) realcompactness and connectedness",
  "authors": [
    "W. W. Comfort",
    "G. Lukács"
  ],
  "comment": "v3 (published version)",
  "journal": "Journal of Lie Theory 20 (2010) 347-374",
  "categories": [
    "math.GN",
    "math.GR"
  ],
  "abstract": "A theorem of A. Weil asserts that a topological group embeds as a (dense) subgroup of a locally compact group if and only if it contains a non-empty precompact open set; such groups are called locally precompact. Within the class of locally precompact groups, the authors classify those groups with the following topological properties: Dieudonn\\'e completeness; local realcompactness; realcompactness; hereditary realcompactness; connectedness; local connectedness; zero-dimensionality. They also prove that an abelian locally precompact group occurs as the quasi-component of a topological group if and only if it is precompactly generated, that is, it is generated algebraically by a precompact subset.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-05-04T11:54:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A05",
      "54H11",
      "22B05",
      "22C05"
    ],
    "keywords": [
      "connectedness",
      "abelian locally precompact group occurs",
      "non-empty precompact open set",
      "topological group",
      "hereditary realcompactness"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.2258C"
    }
  }
}