{
  "id": "1301.0688",
  "version": "v1",
  "published": "2013-01-04T08:45:26.000Z",
  "updated": "2013-01-04T08:45:26.000Z",
  "title": "On the boundary of closed convex sets in $E^{n}$",
  "authors": [
    "M. Beltagy",
    "S. Shenawy"
  ],
  "categories": [
    "math.MG",
    "math.DG"
  ],
  "abstract": "In this article a class of closed convex sets in the Euclidean $n$-space which are the convex hull of their profiles is described. Thus a generalization of Krein-Milman theorem\\cite{Lay:1982} to a class of closed non-compact convex sets is obtained. Sufficient and necessary conditions for convexity, affinity and starshapedness of a closed set and its boundary have been derived in terms of their boundary points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-04T08:45:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C42",
      "52A20"
    ],
    "keywords": [
      "closed convex sets",
      "closed non-compact convex sets",
      "necessary conditions",
      "convex hull",
      "boundary points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.0688B"
    }
  }
}