{
  "id": "1905.10287",
  "version": "v1",
  "published": "2019-05-24T15:31:25.000Z",
  "updated": "2019-05-24T15:31:25.000Z",
  "title": "Selectors for dense subsets of function spaces",
  "authors": [
    "Lev Bukovský",
    "Alexander V. Osipov"
  ],
  "comment": "26 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "Let $USC^*_p(X)$ be the topological space of real upper semicontinuous bounded functions defined on $X$ with the subspace topology of the product topology on ${}^X\\mathbb{R}$. $\\tilde\\Phi^{\\uparrow},\\tilde\\Psi^{\\uparrow}$ are the sets of all upper sequentially dense, upper dense or pointwise dense subsets of $USC^*_p(X)$, respectively. We prove several equivalent assertions to the assertion $USC^*_p(X)$ satisfies the selection principles $S_1(\\tilde\\Phi^{\\uparrow},\\tilde\\Psi^{\\uparrow})$, including a condition on the topological space $X$. We prove similar results for the topological space $C^*_p(X)$ of continuous bounded functions. Similar results hold true for the selection principles $S_{fin}(\\tilde\\Phi^{\\uparrow},\\tilde\\Psi^{\\uparrow})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-24T15:31:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "function spaces",
      "topological space",
      "selection principles",
      "similar results hold true",
      "real upper semicontinuous bounded functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}