{
  "id": "0905.0373",
  "version": "v1",
  "published": "2009-05-04T12:42:33.000Z",
  "updated": "2009-05-04T12:42:33.000Z",
  "title": "Continuity of set-valued maps revisited in the light of tame geometry",
  "authors": [
    "Aris Daniilidis",
    "C. H. Jeffrey Pang"
  ],
  "comment": "21 pages, 2 figures",
  "journal": "J. London Math. Soc. (2011) 83(3): 637-658",
  "doi": "10.1112/jlms/jdq084",
  "categories": [
    "math.OC",
    "math.CA"
  ],
  "abstract": "Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result, depending on stratification techniques, holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-04T12:42:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J53",
      "14P10",
      "57N80",
      "54C60",
      "58C07"
    ],
    "keywords": [
      "tame geometry",
      "set-valued maps",
      "continuity",
      "type results concerning local minima",
      "sard type results concerning local"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.0373D"
    }
  }
}