{
  "id": "1509.02326",
  "version": "v1",
  "published": "2015-09-08T11:19:52.000Z",
  "updated": "2015-09-08T11:19:52.000Z",
  "title": "Quasiopen and p-path open sets, and characterizations of quasicontinuity",
  "authors": [
    "Anders Björn",
    "Jana Björn",
    "Jan Malý"
  ],
  "comment": "17 pages",
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "In this paper we give various characterizations of quasiopen sets and quasicontinuous functions on metric spaces. For complete metric spaces equipped with a doubling measure supporting a p-Poincar\\'e inequality we show that quasiopen and p-path open sets coincide. Under the same assumptions we show that all Newton-Sobolev functions on quasiopen sets are quasicontinuous.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-08T11:19:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31E05",
      "28A05",
      "30L99",
      "31C15",
      "31C40",
      "31C45",
      "46E35"
    ],
    "keywords": [
      "characterizations",
      "quasiopen sets",
      "p-path open sets coincide",
      "quasicontinuity",
      "complete metric spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}