{
  "id": "1209.0847",
  "version": "v2",
  "published": "2012-09-05T02:09:55.000Z",
  "updated": "2012-09-10T12:13:02.000Z",
  "title": "On Hereditarily Normal Topological Groups",
  "authors": [
    "Raushan Buzyakova"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "In this paper we investigate hereditarily normal topological groups and their subspaces. We prove that every compact subspace of a hereditarily normal topological group is metrizable. To prove this statement we first show that a hereditarily normal topological group with a non-trivial convergent sequence has $G_\\delta$-diagonal. This implies, in particular, that every countably compact subset of a hereditarily normal topological group with a non-trivial convergent sequence is metrizable. Another corollary is that under the Proper Forcing Axiom, every countably compact subset of a hereditarily normal topological group is metrizable.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-10T12:13:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H11",
      "22A05",
      "54D15"
    ],
    "keywords": [
      "hereditarily normal topological group",
      "non-trivial convergent sequence",
      "countably compact subset",
      "compact subspace",
      "proper forcing axiom"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.0847B"
    }
  }
}