{
  "abstract": "We show that the homeomorphism groups of the following spaces have precisely $2^{2^{\\aleph_0}}$ maximal subgroups: the rational numbers $\\mathbb{Q}$, the Baire space $\\mathbb{N}^{\\mathbb{N}}$, the space $\\mathbb{N}\\times 2^{\\mathbb{N}}$ where $2^{\\mathbb{N}}$ is the Cantor set, the ordinal $ω^2$ under its order topology, and the Sorgenfrey line $\\mathbb{S}$. More generally, we find sufficient conditions on a group $G$ acting on a topological space which imply that $G$ has at least $2^{2^{\\aleph_0}}$ maximal subgroups. Moreover, if the groups $\\operatorname{Homeo}(\\mathbb{Q})$ and $\\operatorname{Homeo}(\\mathbb{N}^\\mathbb{N})$ are equipped with the pointwise topology, then it is shown that $\\operatorname{Homeo}(\\mathbb{N}^\\mathbb{N})$ has precisely $2^{\\aleph_0}$ open maximal subgroups, and $\\operatorname{Homeo}(\\mathbb{Q})$ has precisely $\\aleph_0$ open maximal subgroups and $2^{\\aleph_0}$ closed maximal subgroups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28211",
  "author_total": 3,
  "authors": [
    {
      "name": "S. Bardyla"
    },
    {
      "name": "L. Elliott"
    },
    {
      "name": "Y. Péresse"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4bfxvmztwmrba.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28211",
  "fulltext_url": null,
  "id": "4bfxvmztwmrba",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28211",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GN"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7204835629",
  "pdf_url": "https://arxiv.org/pdf/2608.28211",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4bfxvmztwmrba.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.28211",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28211"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Maximal subgroups of homeomorphism groups",
  "title_text": "Maximal subgroups of homeomorphism groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/4bfxvmztwmrba",
  "venue": "arXiv",
  "versions": []
}