{
  "id": "1305.6750",
  "version": "v1",
  "published": "2013-05-29T10:18:34.000Z",
  "updated": "2013-05-29T10:18:34.000Z",
  "title": "Equilateral sets in uniformly smooth Banach spaces",
  "authors": [
    "D. Freeman",
    "E. Odell",
    "B. Sari",
    "Th. Schlumprecht"
  ],
  "comment": "11 pages",
  "doi": "10.1112/S0025579313000260",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $X$ be an infinite dimensional uniformly smooth Banach space. We prove that $X$ contains an infinite equilateral set. That is, there exists a constant $\\lambda>0$ and an infinite sequence $(x_i)_{i=1}^\\infty\\subset X$ such that $\\|x_i-x_j\\|=\\lambda$ for all $i\\neq j$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-29T10:18:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46B04"
    ],
    "keywords": [
      "infinite dimensional uniformly smooth banach",
      "dimensional uniformly smooth banach space",
      "infinite equilateral set",
      "infinite sequence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.6750F"
    }
  }
}