{
  "id": "1807.01895",
  "version": "v1",
  "published": "2018-07-05T08:49:42.000Z",
  "updated": "2018-07-05T08:49:42.000Z",
  "title": "On some properties of the space of upper semicontinuous functions",
  "authors": [
    "Alexander V. Osipov",
    "Evgenii G. Pytkeev"
  ],
  "comment": "7 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "For a Tychonoff space $X$, we will be denoted by $USC_{p}(X)$ ($B_1(X)$) a set of all real-valued upper semicontinuous functions (a set of all Baire functions of class 1) defined on $X$ provided with the pointwise convergence topology. In this paper we describe a class of Tychonoff spaces $X$ for which the space $USC_{p}(X)$ is sequentially separable. Unexpectedly, it turns out that this class coincides with the class of spaces for which the strengthened form of the sequential separability of the space $B_1(X)$ holds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-05T08:49:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "properties",
      "tychonoff space",
      "real-valued upper semicontinuous functions",
      "baire functions",
      "pointwise convergence topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}