{
  "id": "1607.04364",
  "version": "v1",
  "published": "2016-07-15T02:50:26.000Z",
  "updated": "2016-07-15T02:50:26.000Z",
  "title": "Normality versus paracompactness in locally compact spaces",
  "authors": [
    "Alan Dow",
    "Franklin D. Tall"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "This note provides a correct proof of the result claimed by the second author that locally compact normal spaces are collectionwise Hausdorff in certain models obtained by forcing with a coherent Souslin tree. A novel feature of the proof is the use of saturation of the non-stationary ideal on \\omega_1, as well as of a strong form of Chang's Conjecture. Together with other improvements, this enables the characterization of locally compact hereditarily paracompact spaces as those locally compact, hereditarily normal spaces that do not include a copy of \\omega_1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-15T02:50:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A35",
      "54D20",
      "54D45",
      "03E35",
      "03E50",
      "03E55",
      "03E57"
    ],
    "keywords": [
      "locally compact spaces",
      "paracompactness",
      "locally compact hereditarily paracompact spaces",
      "coherent souslin tree",
      "locally compact normal spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}