{
  "id": "2110.15496",
  "version": "v4",
  "published": "2021-10-29T02:26:52.000Z",
  "updated": "2022-05-17T15:03:25.000Z",
  "title": "Baire property of space of Baire-one functions",
  "authors": [
    "Alexander V. Osipov"
  ],
  "comment": "30 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "A topological space $X$ is Baire if the Baire Category Theorem holds for $X$, i.e., the intersection of any sequence of open dense subsets of $X$ is dense in $X$. One of the interesting problems for the space $B_1(X)$ of all Baire-one real-valued functions is characterization topological space $X$ for which the function space $B_1(X)$ is Baire. In this paper, we solve this problem, namely, we have obtained a characterization when a function space $B_1(X)$ has the Baire property for any Tychonoff space $X$. Also we proved that $B_1(X)$ is Baire for any $\\gamma$-space $X$. This answers a question posed recently by T. Banakh and S. Gabriyelyan. We also conclude that, it is consistent there are no uncountable separable metrizable space $X$ such that $B_1(X)$ is countable dense homogeneous.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2022-05-17T15:03:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "baire property",
      "baire-one functions",
      "function space",
      "baire category theorem holds",
      "open dense subsets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}