{
  "id": "1908.11693",
  "version": "v1",
  "published": "2019-08-30T12:44:03.000Z",
  "updated": "2019-08-30T12:44:03.000Z",
  "title": "Cardinality Estimations of Sets with Interval Uncertainties in Finite Topological Spaces",
  "authors": [
    "J. F. Peters",
    "I. J. Dochviri"
  ],
  "comment": "6 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "In this paper, we have established boundaries of cardinal numbers of nonempty sets in finite non-$T_1$ topological spaces using interval analysis. For a finite set with known cardinality, we give interval estimations based on the closure and interior of the set. In this paper, we give new results for the cardinalities of non-empty semi-open sets in non-$T_1$ topological spaces as well as in extremely disconnected and hyperconnected topological spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-30T12:44:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A25",
      "05A19"
    ],
    "keywords": [
      "finite topological spaces",
      "interval uncertainties",
      "cardinality estimations",
      "non-empty semi-open sets",
      "nonempty sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}