{
  "id": "1808.00715",
  "version": "v1",
  "published": "2018-08-02T09:04:55.000Z",
  "updated": "2018-08-02T09:04:55.000Z",
  "title": "Complete metric spaces with property (Z) are length metric spaces",
  "authors": [
    "Antonio Avilés",
    "Gonzalo Martínez-Cervantes"
  ],
  "categories": [
    "math.FA",
    "math.GN"
  ],
  "abstract": "We prove that every complete metric space with property (Z) is a length space. These answers questions posed by Garc\\'{i}a-Lirola, Proch\\'{a}zka and Rueda Zoca, and by Becerra Guerrero, L\\'{o}pez-P\\'{e}rez and Rueda Zoca, related to the structure of Lipschitz-free Banach spaces of metric spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-02T09:04:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "54E50"
    ],
    "keywords": [
      "complete metric space",
      "length metric spaces",
      "rueda zoca",
      "lipschitz-free banach spaces",
      "answers questions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}