{
  "id": "1408.5793",
  "version": "v1",
  "published": "2014-08-25T15:12:31.000Z",
  "updated": "2014-08-25T15:12:31.000Z",
  "title": "A metric characterization of snowflakes of Euclidean spaces",
  "authors": [
    "Kyle Kinneberg",
    "Enrico Le Donne"
  ],
  "categories": [
    "math.MG"
  ],
  "abstract": "We give a metric characterization of snowflakes of Euclidean spaces. Namely, a metric space is isometric to $\\mathbb R^n$ equipped with a distance $(d_{\\rm E})^\\epsilon$, for some $n\\in \\mathbb N_0$ and $\\epsilon\\in (0,1]$, where $d_{\\rm E}$ is the Euclidean distance, if and only if it is locally compact, $2$-point isometrically homogeneous, and admits dilations of any factor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-25T15:12:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "euclidean spaces",
      "metric characterization",
      "snowflakes",
      "admits dilations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.5793K"
    }
  }
}