{
  "abstract": "We prove that consistently $ω_1<\\mathfrak{c}$ and there exists a compact space $K$ whose Banach space $C(K)$ of continuous real-valued functions is Grothendieck, has density $ω_1$, and admits no renorming which is strictly convex or sequentially Kadets--Klee.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.13294",
  "author_total": 3,
  "authors": [
    {
      "name": "Todor Manev"
    },
    {
      "name": "Damian Sobota"
    },
    {
      "name": "Lyubomyr Zdomskyy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a4x9d285f5byn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.13294",
  "fulltext_url": null,
  "id": "a4x9d285f5byn",
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  "landing_url": "https://arxiv.org/abs/2606.13294",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.GN"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
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  "openalex": "W7164588907",
  "pdf_url": "https://arxiv.org/pdf/2606.13294",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a4x9d285f5byn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2606.13294",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.13294"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "A small Banach space $C(K)$ without nice renormings",
  "title_text": "A small Banach space C(K) without nice renormings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/a4x9d285f5byn",
  "venue": "arXiv",
  "versions": []
}