{
  "id": "math/9907162",
  "version": "v1",
  "published": "1999-07-24T12:52:11.000Z",
  "updated": "1999-07-24T12:52:11.000Z",
  "title": "On imbedding of closed 2-dimensional disks into $R^2$",
  "authors": [
    "Eugene Polulyakh"
  ],
  "comment": "LaTeX-2e document, 28 pages",
  "journal": "Methods of Func. An. and Topology - 1998 - N 2 - P. 76-94",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Let $X$ be a topological space, $U$ -- opened subset of $X$. We will say that point $x \\in \\partial U$ is {\\it accessible} from $U$ if there exists continuous injective mapping $\\phi : I \\to \\Cl D$ such that $\\phi(1)=x$, $\\phi([0,1)) \\subset \\Int U$. We proove the next main theorem. The following conditions are neccesary and suffficient for a compact subset $D$ of $R^2$ with a nonempty interior $\\Int D$ to be homeomorphic to a closed 2-dimensional disk: 1) sets $\\Int D$ and $R^2 \\setminus D$ are connected; 2) any $x \\in \\partial D$ is accessible both from $\\Int D$ and from $R^2 \\setminus D$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-07-24T12:52:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E35",
      "57M50",
      "57N35"
    ],
    "keywords": [
      "main theorem",
      "compact subset",
      "nonempty interior",
      "topological space",
      "suffficient"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......7162P"
    }
  }
}