{
  "id": "math/0201077",
  "version": "v5",
  "published": "2002-01-10T19:18:11.000Z",
  "updated": "2007-02-15T15:18:06.000Z",
  "title": "A family of pseudo metrics on B^3 and its application",
  "authors": [
    "Young Deuk Kim"
  ],
  "comment": "14 pages, 5 figures, A section of v3 is appeared on Rocky Mountain Journal of Mathematics 36(2006) no.6 1927-1935. Similar construction is in GN/0702453",
  "categories": [
    "math.GN",
    "math.GT"
  ],
  "abstract": "Let B^3 be the closed unit ball in R^3 and S^2 its boundary. We define a family of pseudo metrics on B^3. As an application, We prove that for any countable-to-one function f:S^2\\to [0,a], the set NM^n_f={x\\in S^2 | there exists y\\in S^2 such that f(x)-f(y)>nd_E(x,y)} is uncountable for all natural number n, where d_E is the Euclidean metric on R^3.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2007-02-15T15:18:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N05",
      "57M40"
    ],
    "keywords": [
      "pseudo metrics",
      "application",
      "closed unit ball",
      "countable-to-one function",
      "natural number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......1077D"
    }
  }
}