{
  "abstract": "A space is feebly compact if every locally finite family of nonempty open subsets of it is finite; a Tychonoff space is feebly compact if and only if it is pseudocompact. M. Tkachenko asked whether a regular feebly compact semitopological group is a topological group provided that it is separable, has countable tightness, or is a $k$-space; for Tychonoff groups the answer is known to be positive. We answer this question in the separable case: every regular separable feebly compact semitopological group is a topological group. The proof is based on the following result: if $X$ is a separable Baire space, $Y$ is a feebly compact space and $Z$ is a regular space, then every separately continuous map $X\\times Y\\to Z$ is strongly quasicontinuous. Unlike the known approaches for Tychonoff spaces, the proof does not use real-valued functions. More generally, every regular separable semitopological group which is $Γ^{BM}_o$-nonmeager, a Baire-type property defined by a modification of the Banach-Mazur game, is a topological group. This class of groups contains all regular separable Baire groups which are feebly $p$-spaces; feebly $p$-spaces form a wider class of spaces, which contains all feebly compact spaces and all $p$-spaces. The results remain valid for spaces satisfying the assumptions locally. In particular, every regular locally separable locally feebly compact semitopological group is a topological group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04891",
  "author_total": 1,
  "authors": [
    {
      "name": "Evgenii Reznichenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9a07q3zfk57yx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04891",
  "fulltext_url": null,
  "id": "9a07q3zfk57yx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04891",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04891",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9a07q3zfk57yx.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04891",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04891"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Separately continuous maps into regular spaces and continuity of operations in separable semitopological groups",
  "title_text": "Separately continuous maps into regular spaces and continuity of operations in separable semitopological groups",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/9a07q3zfk57yx",
  "venue": "arXiv",
  "versions": []
}