{
  "id": "1903.10001",
  "version": "v1",
  "published": "2019-03-24T15:30:00.000Z",
  "updated": "2019-03-24T15:30:00.000Z",
  "title": "Cantor's intersection theorem in the setting of $\\mathcal{F}$-metric spaces",
  "authors": [
    "Sumit Som",
    "Lakshmi Kanta Dey"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "This paper deals with an open problem posed by Jleli and Samet in \\cite[\\, M.~Jleli and B.~Samet, On a new generalization of metric spaces, J. Fixed Point Theory Appl, 20(3) 2018]{JS1}. In \\cite[\\, Remark 5.1]{JS1} They asked whether the Cantor's intersection theorem can be extended to $\\mathcal{F}$-metric spaces or not. In this manuscript we give an affirmative answer to this open question. We also show that the notions of compactness, totally boundedness in the setting of $\\mathcal{F}$-metric spaces are equivalent to that of usual metric spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-24T15:30:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H10",
      "54A20",
      "54E50"
    ],
    "keywords": [
      "cantors intersection theorem",
      "usual metric spaces",
      "fixed point theory appl",
      "open problem",
      "paper deals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}