{
  "id": "1812.09542",
  "version": "v1",
  "published": "2018-12-22T15:16:48.000Z",
  "updated": "2018-12-22T15:16:48.000Z",
  "title": "Coincidence and noncoincidence of dimensions in compact subsets of $[0,1]$",
  "authors": [
    "Andrew Mitchell",
    "Lars Olsen"
  ],
  "comment": "18 pages",
  "categories": [
    "math.MG"
  ],
  "abstract": "We show that given any six numbers $r,s,t,u,v,w \\in (0,1]$ satisfying $r \\leq s \\leq \\min(t,u) \\leq \\max(t,u) \\leq v \\leq w$, it is possible to construct a compact subset of $[0,1]$ with Hausdorff dimension equal to $r$, lower modified box dimension equal to $s$, packing dimension equal to $t$, lower box dimension equal to $u$, upper box dimension equal to $v$ and Assouad dimension equal to $w$. Moreover, the set constructed is an $r$-Hausdorff set and a $t$-packing set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-22T15:16:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A78",
      "28A80"
    ],
    "keywords": [
      "compact subset",
      "upper box dimension equal",
      "lower box dimension equal",
      "noncoincidence",
      "lower modified box dimension equal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}