{
  "id": "2401.15923",
  "version": "v2",
  "published": "2024-01-29T07:29:13.000Z",
  "updated": "2024-09-02T14:55:59.000Z",
  "title": "Dieudonné completeness of function spaces",
  "authors": [
    "Mikhail Al'perin",
    "Alexander V. Osipov"
  ],
  "comment": "10 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "A space is called Dieudonn\\'{e} complete if it is complete relative to the maximal uniform structure compatible with its topology. In this paper, we investigated when the function space $C(X,Y)$ of all continuous functions from a topological space $X$ into a uniform space $Y$ with the topology of uniform convergence on a family of subsets of $X$ is Dieudonn\\'{e} complete. Also we proved a generalization of the Eberlein-\\v{S}mulian theorem to the class of Banach spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-09-02T14:55:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "function space",
      "completeness",
      "maximal uniform structure compatible",
      "uniform convergence",
      "uniform space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}