{
  "id": "1803.07633",
  "version": "v1",
  "published": "2018-03-20T20:07:07.000Z",
  "updated": "2018-03-20T20:07:07.000Z",
  "title": "The Menger and projective Menger properties of function spaces with the set-open topology",
  "authors": [
    "Alexander V. Osipov"
  ],
  "comment": "11 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "For a Tychonoff space $X$ and a family $\\lambda$ of subsets of $X$, we denote by $C_{\\lambda}(X)$ the space of all real-valued continuous functions on $X$ with the set-open topology. In this paper, we study the Menger and projective Menger properties of a Hausdorff space $C_{\\lambda}(X)$. Our main results state that if $\\lambda$ is a $\\pi$-network of $X$ then (1) $C_{\\lambda}(X)$ is Menger space if and only if it is $\\sigma$-compact, if $\\lambda$ is a $\\pi$-network of finite subsets of $X$ then (2) $C_{\\lambda}(X)$ is projective Menger space if and only if it is $\\sigma$-pseudocompact.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-20T20:07:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "projective menger properties",
      "set-open topology",
      "function spaces",
      "main results state",
      "projective menger space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}