{
  "id": "2308.08400",
  "version": "v1",
  "published": "2023-08-16T14:40:26.000Z",
  "updated": "2023-08-16T14:40:26.000Z",
  "title": "On a problem of Mazur and Sternbach",
  "authors": [
    "Giuliano Basso"
  ],
  "comment": "5 pages",
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "We give an affirmative answer to problem 155 form the \"Scottish Book\" due to Mazur and Sternbach. In modern terminology they asked if every bijective local isometry between two real Banach spaces is always a global isometry. Recently, an affirmative answer in the separable case has been obtained by M. Mori, using techniques related to the Mazur--Ulam theorem. In this short note, we use a different approach motivated by recent advances in metric geometry to completely settle Mazur and Sternbach's question.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-16T14:40:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real banach spaces",
      "affirmative answer",
      "global isometry",
      "bijective local isometry",
      "mazur-ulam theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}