{
  "id": "math/0203233",
  "version": "v1",
  "published": "2002-03-22T14:17:04.000Z",
  "updated": "2002-03-22T14:17:04.000Z",
  "title": "A Characterization of Similarity Maps Between Euclidean Spaces Related to the Beckman--Quarles Theorem",
  "authors": [
    "Jobst Heitzig"
  ],
  "comment": "5 pages",
  "categories": [
    "math.MG",
    "math.GN"
  ],
  "abstract": "It is shown that each continuous transformation $h$ from Euclidean $m$-space ($m>1$) into Euclidean $n$-space that preserves the equality of distances (that is, fulfils the implication $|x-y|=|z-w|\\Rightarrow|h(x)-h(y)|=|h(z)-h(w)|$) is a similarity map. The case of equal dimensions already follows from the Beckman--Quarles Theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-03-22T14:17:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51F20",
      "51F25",
      "15A04"
    ],
    "keywords": [
      "euclidean spaces",
      "beckman-quarles theorem",
      "similarity map",
      "characterization",
      "equal dimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......3233H"
    }
  }
}