{
  "id": "2106.15192",
  "version": "v1",
  "published": "2021-06-29T09:24:52.000Z",
  "updated": "2021-06-29T09:24:52.000Z",
  "title": "Completeness in topological vector spaces and filters on N",
  "authors": [
    "Vladimir Kadets",
    "Dmytro Seliutin"
  ],
  "comment": "15 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study completeness of a topological vector space with respect to different filters on the set N of all naturals. In the metrizable case all these kinds of completeness are the same, but in non-metrizable case the situation changes. For example, a space may be complete with respect to one ultrafilter on N, but incomplete with respect to another. Our study was motivated by [Aizpuru, List\\'an-Garc\\'ia and Rambla-Barreno; Quaest. Math., 2014] and [List\\'an-Garc\\'ia; Bull. Belg. Math. Soc. Simon Stevin, 2016] where for normed spaces the equivalence of the ordinary completeness and completeness with respect to f-statistical convergence was established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-29T09:24:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "40A35",
      "46A03",
      "54A20"
    ],
    "keywords": [
      "topological vector space",
      "situation changes",
      "study completeness",
      "listan-garcia",
      "simon stevin"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}