{
  "id": "1810.11278",
  "version": "v1",
  "published": "2018-10-26T11:48:08.000Z",
  "updated": "2018-10-26T11:48:08.000Z",
  "title": "Supports and extreme points in Lipschitz-free spaces",
  "authors": [
    "Ramón J. Aliaga",
    "Eva Pernecká"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "For a complete metric space $M$, we prove that the finitely supported extreme points of the unit ball of the Lipschitz-free space $\\mathcal{F}(M)$ are precisely the elementary molecules $(\\delta(p)-\\delta(q))/d(p,q)$ defined by pairs of points $p,q$ in $M$ such that the triangle inequality $d(p,q)<d(p,r)+d(q,r)$ is strict for any $r\\in M$ different from $p$ and $q$. To this end, we show that the class of Lipschitz-free spaces over closed subsets of $M$ is closed under arbitrary intersections when $M$ has finite diameter, and that this allows a natural definition of the support of elements of $\\mathcal{F}(M)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-26T11:48:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "54E50"
    ],
    "keywords": [
      "lipschitz-free space",
      "complete metric space",
      "finitely supported extreme points",
      "elementary molecules",
      "triangle inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}