{
  "id": "1901.10054",
  "version": "v1",
  "published": "2019-01-18T20:15:20.000Z",
  "updated": "2019-01-18T20:15:20.000Z",
  "title": "On the cardinality of $π(δ)$",
  "authors": [
    "Attila Losonczi"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We prove that the cardinality of transitive quasi-uniformities in a quasi-proximity class is at least $2^{2^{\\aleph_0}}$ if there exist at least two transitive quasi-uniformities in the class. The transitive elements of $\\pi(\\delta)$ are characterized if ${\\cal V}_{\\delta}$ is transitive, and in this case we give a condition when there exists a unique transitive quasi-uniformity in $\\pi(\\delta)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-18T20:15:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cardinality",
      "quasi-proximity class",
      "unique transitive quasi-uniformity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}