{
  "abstract": "A topological space is $\\varkappa$-Fréchet--Urysohn if every point in the closure of an open set $U$ is the limit of a sequence of points of $U$. We prove that every $\\varkappa$-Fréchet--Urysohn subgroup and every Baire subgroup of the free topological group on a Tychonoff space $X$ in any full variety of topological groups (in particular, of the free topological group $F(X)$, the free Abelian topological group $A(X)$, and the free Boolean topological group $B(X)$) is discrete. In particular, each of these groups is $\\varkappa$-Fréchet--Urysohn (or Baire) only if $X$ is discrete, and all their metrizable and even Fréchet--Urysohn subgroups are discrete. Along the way we characterize strongly $\\varkappa$-Fréchet--Urysohn spaces in the spirit of Michael's theorem and study countable families of closed sets absorbing convergent sequences in $\\varkappa$-Fréchet--Urysohn spaces and groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07401",
  "author_total": 3,
  "authors": [
    {
      "name": "Arkady Leiderman"
    },
    {
      "name": "Evgenii Reznichenko"
    },
    {
      "name": "Ol'ga Sipacheva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6xpma22qdcv6q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07401",
  "fulltext_url": null,
  "id": "6xpma22qdcv6q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07401",
  "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"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7220894997",
  "pdf_url": "https://arxiv.org/pdf/2610.07401",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6xpma22qdcv6q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07401",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07401"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "$\\varkappa$-Fréchet--Urysohn and Baire subgroups of free topological groups",
  "title_text": "varkappa-Fréchet--Urysohn and Baire subgroups of free topological groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/6xpma22qdcv6q",
  "venue": "arXiv",
  "versions": []
}