{
  "id": "1904.09034",
  "version": "v1",
  "published": "2019-04-18T22:36:16.000Z",
  "updated": "2019-04-18T22:36:16.000Z",
  "title": "A \"rare'' plane set with Hausdorff dimension 2",
  "authors": [
    "Vladimir Eiderman",
    "Michael Larsen"
  ],
  "comment": "4 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove that for every at most countable family $\\{f_k(x)\\}$ of real functions on $[0,1)$ there is a single-valued real function $F(x)$, $x\\in[0,1)$, such that the Hausdorff dimension of the graph $\\Gamma$ of $F(x)$ equals 2, and for every $C\\in\\mathbb R$ and every $k$, the intersection of $\\Gamma$ with the graph of the function $f_k(x)+C$ consists of at most one point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-18T22:36:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A78"
    ],
    "keywords": [
      "hausdorff dimension",
      "plane set",
      "single-valued real function",
      "intersection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}