{
  "id": "2302.14492",
  "version": "v1",
  "published": "2023-02-28T11:19:25.000Z",
  "updated": "2023-02-28T11:19:25.000Z",
  "title": "On covering dimension and sections of vector bundles",
  "authors": [
    "M. C. Crabb"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "An elementary result in point-set topology is used, with knowledge of the mod $2$ cohomology of real projective spaces, to establish classical results of Lebesgue and Knaster-Kuratowski-Mazurkiewicz, as well as the topological central point theorem of Karasev, which is applied to deduce results of Helly-Lov\\'asz, B\\'ar\\'any and Tverberg",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-28T11:19:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R25",
      "54F45",
      "55M10",
      "55R40",
      "55M30"
    ],
    "keywords": [
      "vector bundles",
      "covering dimension",
      "topological central point theorem",
      "point-set topology",
      "elementary result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}