{
  "id": "1808.04637",
  "version": "v1",
  "published": "2018-08-14T11:37:14.000Z",
  "updated": "2018-08-14T11:37:14.000Z",
  "title": "The Bohr compactification of an abelian group as a quotient of its Stone-Čech compactification",
  "authors": [
    "Pavol Zlatoš"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We will prove that, for any abelian group $G$, the canonical (surjective and continuous) mapping $\\btG \\to \\fbG$ from the Stone-\\v{C}ech compactification $\\btG$ of $G$ to its Bohr compactfication $\\fbG$ is a homomorphism with respect to the semigroup operation on $\\btG$, extending the multiplication on $G$, and the group operation on $\\fbG$. Moreover, the Bohr compactification $\\fbG$ is canonically isomorphic (both in algebraic and topological sense) to the quotient of $\\btG$ with respect to the least closed congruence relation on $\\btG$ merging all the \\textit{Schur ultrafilters} on $G$ into the unit of \\,$G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-14T11:37:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A15",
      "22C05",
      "43A40",
      "43A60",
      "54H11"
    ],
    "keywords": [
      "abelian group",
      "bohr compactification",
      "stone-čech compactification",
      "bohr compactfication",
      "closed congruence relation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}