{
  "abstract": "Assuming that $\\mathcal{P}(ω)$ is tightly $σ$-filtered, we prove that $C(ω^*)$ fails the ball fixed point property. This axiom holds under the continuum hypothesis and in the $\\aleph_2$-Cohen model. The proof shows that the Stone space of the countable--cocountable algebra $\\operatorname{Cc}(ω_1)$ is a continuous retract of $ω^*$ and uses the equivalence between tight $σ$-filteredness of $\\operatorname{Cc}(ω_1)$ and of $\\mathcal{P}(ω)$. We also prove that the quotient of a tightly $σ$-filtered Boolean algebra $B$ with the countable separation property by an $\\aleph_1$-generated $P$-ideal is a Boolean retract of $B$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16672",
  "author_total": 2,
  "authors": [
    {
      "name": "Antonio Avilés"
    },
    {
      "name": "Maurício Rossetto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/27pfkbvkt9m52.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16672",
  "fulltext_url": null,
  "id": "27pfkbvkt9m52",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16672",
  "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"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7221753265",
  "pdf_url": "https://arxiv.org/pdf/2610.16672",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/27pfkbvkt9m52.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16672",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16672"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Tight $σ$-filtrations and the BFPP of $C(ω^*)$",
  "title_text": "Tight σ-filtrations and the BFPP of C(ω^*)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/27pfkbvkt9m52",
  "venue": "arXiv",
  "versions": []
}