{
  "id": "1906.08498",
  "version": "v1",
  "published": "2019-06-20T08:28:24.000Z",
  "updated": "2019-06-20T08:28:24.000Z",
  "title": "A T_0 Compactification Of A Tychonoff Space Using The Rings Of Baire One Functions",
  "authors": [
    "A. Deb Ray",
    "Atanu Mondal"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "In this article, we continue our study of Baire one functions on a topological space $X$, denoted by $B_1(X)$ and extend the well known M. H. Stones's theorem from $C(X)$ to $B_1(X)$. Introducing the structure space of $B_1(X)$, it is observed that $X$ may not be embedded inside this structure space. This observation inspired us to build a space $\\MMM(B_1(X))/\\sim$, from the structure space of $B_1(X)$ and to show that $X$ is densely embedded in $\\MMM(B_1(X))/\\sim$. It is further established that it is a $T_0$-compactification of $X$. Such compactification of $X$ possesses the extension property for continuous functions, though it lacks Hausdorffness in general. Therefore, it is natural to search for condition(s) under which it becomes Hausdorff. In the last section, a set of necessary and sufficient conditions for such compactification to become a Stone-Ceck compatification, is finally arrived at.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-20T08:28:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A21",
      "54C30",
      "13A15",
      "54C50",
      "54D35"
    ],
    "keywords": [
      "tychonoff space",
      "compactification",
      "structure space",
      "stoness theorem",
      "extension property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}