{
  "id": "math/0408207",
  "version": "v4",
  "published": "2004-08-16T13:51:21.000Z",
  "updated": "2005-05-23T22:17:28.000Z",
  "title": "Boundedness in generalized Šerstnev PN spaces",
  "authors": [
    "Bernardo Lafuerza-Guillen",
    "Jose L. Rodriguez"
  ],
  "comment": "19 pages. Some parts have been revised and some new results are included",
  "categories": [
    "math.FA",
    "math.GN"
  ],
  "abstract": "The motivation of this paper is a suggestion by H\\\"ole of comparing the notions of $\\D$-boundedness and boundedness in Probabilistic Normed spaces (briefly PN spaces), with non necessarily continuous triangle functions. Such spaces are here called ``pre-PN spaces''. Some results on \\v{S}erstnev spaces due to B. Lafuerza, J. A. Rodriguez, and C. Sempi, are here extended to generalized \\v{S}erstnev spaces (these are pre-PN spaces satisfying a more general \\v{S}erstnev condition). We also prove some facts on PN spaces (with continuous triangle functions). First, a connection between fuzzy normed spaces defined by Felbin and certain \\v{S}erstnev PN spaces is established. We further observe that topological vector PN spaces are $F$-normable and paranormable, and also that locally convex topological vector PN spaces are bornological. This last fact allows to describe continuous linear operators between certain generalized \\v{S}erstnev spaces in terms of bounded subsets.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2005-05-23T22:17:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54E70",
      "46S50"
    ],
    "keywords": [
      "boundedness",
      "convex topological vector pn spaces",
      "pre-pn spaces",
      "locally convex topological vector pn"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8207L"
    }
  }
}