{
  "abstract": "A compactification of the discrete space $ω$ of all integers is called symmetric if it is the quotient space obtained by gluing together the remainders of two copies of some other compactification of $ω$. This is a generalization of both a convergent sequence, which is in a way the minimal symmetric compactification of $ω$, and the Arkhangel'ski\\uı--Bereznitski\\uı--Schachermayer space studied in $C_p$-theory, which is in a sense the maximal symmetric compactification of $ω$. We investigate symmetric compactifications of $ω$ and their relations to the Separable Quotient Problem for spaces $C_p(X)$ and to the existence of Josefson--Nissenzweig sequences of finitely supported Borel measures on spaces $X$, in particular with supports of bounded size. Further, we reduce the Separable Quotient Problem for spaces $C_p(K)$, $K$ compact, to the case when $K$ is a totally asymmetric compactification of $ω$. Our results shed some new light on the Grothendieck property of Banach spaces $C(K)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18904",
  "author_total": 2,
  "authors": [
    {
      "name": "Zdeněk Silber"
    },
    {
      "name": "Damian Sobota"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/byg7qn79g28jp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18904",
  "fulltext_url": null,
  "id": "byg7qn79g28jp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18904",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.GN"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7213494822",
  "pdf_url": "https://arxiv.org/pdf/2609.18904",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/byg7qn79g28jp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18904",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18904"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Symmetric compactifications of the integers and separable quotients of spaces $C_p(X)$",
  "title_text": "Symmetric compactifications of the integers and separable quotients of spaces C_p(X)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/byg7qn79g28jp",
  "venue": "arXiv",
  "versions": []
}