{
  "id": "1704.05279",
  "version": "v1",
  "published": "2017-04-18T11:34:49.000Z",
  "updated": "2017-04-18T11:34:49.000Z",
  "title": "I-Completeness in Function Spaces",
  "authors": [
    "Amar Kumar Banerjee",
    "Apurba Banerjee"
  ],
  "comment": "11 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "In this paper we have studied the idea of ideal completeness of function spaces Y to the power X with respect to pointwise uniformity and uniformity of uniform convergence. Further involving topological structure on X we have obtained relationships between the uniformity of uniform convergence on compacta on Y to the power X and uniformity of uniform convergence on Y to the power X in terms of I-Cauchy condition and I-convergence of a net. Also using the notion of a k-space we have given a sufficient condition for C(X,Y) to be ideal complete with respect to the uniformity of uniform convergence on compacta.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-18T11:34:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A20",
      "40A35",
      "54E15"
    ],
    "keywords": [
      "function spaces",
      "uniform convergence",
      "uniformity",
      "i-completeness",
      "ideal completeness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}