{
  "id": "0905.2616",
  "version": "v2",
  "published": "2009-05-15T20:30:08.000Z",
  "updated": "2012-08-31T23:17:36.000Z",
  "title": "Proper actions on topological groups: Applications to quotient spaces",
  "authors": [
    "Sergey A. Antonyan"
  ],
  "comment": "In the proof of Proposition 3.1 of the previous version there is a small gap. To correct the gap, at the end of the proof (now Proposition 3.2) one should just reference to a newly added Lemma 3.1 for the fact that Ux is a G-small set. Results unchanged. arXiv admin note: substantial text overlap with arXiv:1103.1407",
  "journal": "Proc. AMS, vol. 138, no. 10 (2010), 3707-3716",
  "categories": [
    "math.GN",
    "math.GT"
  ],
  "abstract": "Let X be a Hausdorff topological group and G a locally compact subgroup of X. We show that the natural action of G on X is proper in the sense of R. Palais. This is applied to prove that there exists a closed set F of X such that FG=X and the restriction of the quotient projection X -> X/G to F is a perfect map F -> X/G. This is a key result to prove that many topological properties (among them, paracompactness and normality) are transferred from X to ferred from X/G to X. Yet another application leads to the inequality dim X<= dim X/G + dim G for every paracompact group X and its locally compact subgroup G.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-31T23:17:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A05",
      "54H11"
    ],
    "keywords": [
      "quotient spaces",
      "proper actions",
      "locally compact subgroup",
      "application",
      "hausdorff topological group"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.2616A"
    }
  }
}