{
  "abstract": "We prove that, for a compact Hausdorff space $K$, the real Banach space $C(K)$ has the ball fixed point property if and only if $K$ is extremally disconnected. The new implication is obtained by constructing a fixed-point-free nonexpansive self-map of the whole closed unit ball whenever $K$ is a compact $F$-space which is not extremally disconnected. The construction uses a transfinite contractive propagation system with two increasing profiles. A successor--limit delay preserves their tail constraint and has no subsolution in the profile domain. Analysis records boundary deficits; positive operators on ordinal $C_0$-spaces and a common center determined by the two tails yield a nonexpansive synthesis satisfying an order domination inequality. The required topological families are obtained from a gap in a maximal Boolean chain in the zero-dimensional case, and from a transfinite extension of signs otherwise. The argument works in ZFC and resolves the question posed by Avilés, Japón, Lennard, Martínez-Cervantes, and Stawski.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16318",
  "author_total": 1,
  "authors": [
    {
      "name": "Cleon S. Barroso"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fna2ra7ycc806.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16318",
  "fulltext_url": null,
  "id": "fna2ra7ycc806",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16318",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7213403020",
  "pdf_url": "https://arxiv.org/pdf/2609.16318",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fna2ra7ycc806.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16318",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16318"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Transfinite contractive propagation and the ball fixed point property in \\texorpdfstring{$C(K)$}{C(K)}",
  "title_text": "Transfinite contractive propagation and the ball fixed point property in \\texorpdfstring{C(K)}{C(K)}",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/fna2ra7ycc806",
  "venue": "arXiv",
  "versions": []
}