{
  "id": "2207.11973",
  "version": "v1",
  "published": "2022-07-25T08:23:41.000Z",
  "updated": "2022-07-25T08:23:41.000Z",
  "title": "Blaschke, Separation Theorems and some Topological Properties for Orthogonally Convex Sets",
  "authors": [
    "Phan Thanh An",
    "Nguyen Thi Le"
  ],
  "comment": "17 pages, 10 figures",
  "categories": [
    "math.OC",
    "cs.CG"
  ],
  "abstract": "In this paper, we deal with analytic and geometric properties of orthogonally convex sets. We establish a Blaschke-type theorem for path-connected and orthogonally convex sets in the plane using orthogonally convex paths. The separation of these sets is established using suitable grids. Consequently, a closed and orthogonally convex set is represented by the intersection of staircase-halfplanes in the plane. Some topological properties of orthogonally convex sets in dimensional spaces are also given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-25T08:23:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B25",
      "32F27",
      "52A10",
      "52A30"
    ],
    "keywords": [
      "orthogonally convex set",
      "topological properties",
      "separation theorems",
      "blaschke-type theorem",
      "orthogonally convex paths"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}