{
  "id": "0911.3985",
  "version": "v2",
  "published": "2009-11-20T07:52:21.000Z",
  "updated": "2010-05-28T11:44:20.000Z",
  "title": "Direct limit topologies in the categories of topological groups and of uniform spaces",
  "authors": [
    "Taras Banakh",
    "Dusan Repovs"
  ],
  "comment": "20 pages",
  "journal": "Tohoku Math. J. 64:1 (2012), 1-24",
  "categories": [
    "math.GN",
    "math.GR"
  ],
  "abstract": "We study the topological structure of the direct limit $\\glim G_n$ of a tower of topological groups $(G_n)$ in the category of topological groups and show that under some conditions on the tower $(G_n)$ the topology of $\\glim G_n$ coincides with the topology of the direct limit $\\ulim G_n$ of the groups $G_n$ endowed with the Roelcke uniformity in the category of uniform spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-05-28T11:44:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18A30",
      "22A05",
      "54B30",
      "54E15",
      "54H11"
    ],
    "keywords": [
      "direct limit topologies",
      "topological groups",
      "uniform spaces",
      "roelcke uniformity",
      "topological structure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.3985B"
    }
  }
}