{
  "id": "1806.05890",
  "version": "v1",
  "published": "2018-06-15T10:27:56.000Z",
  "updated": "2018-06-15T10:27:56.000Z",
  "title": "Topological developments of $\\mathcal{F}$-metric spaces",
  "authors": [
    "Ashis Bera",
    "Lakshmi Kanta Dey",
    "Hiranmoy Garai",
    "Ankush Chanda"
  ],
  "comment": "13 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this manuscript, we claim that the newly introduced $\\mathcal{F}$-metric spaces are Hausdorff and also first countable. Moreover, we assert that every separable $\\mathcal{F}$-metric space is second countable. Additionally, we acquire some interesting fixed point results concerning altering distance functions for contractive-type mappings and Kannan-type contractive mappings in this exciting context. However, most of the findings are well-furnished by several non-trivial numerical examples. Finally, we raise an open problem regarding the metrizability of such kind of spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-15T10:27:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H10",
      "54H25"
    ],
    "keywords": [
      "metric space",
      "topological developments",
      "fixed point results concerning",
      "point results concerning altering distance",
      "results concerning altering distance functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}