{
  "abstract": "We answer in ZFC a question of N. Carlson by constructing a zero-dimensional Tychonoff space $X$, with exactly one non-isolated point, for which every point admits a decreasing local $π$-base and \\[ πχ(X)=πχ_{\\mathrm l}(X)=ω<πχ_{\\mathrm c}(X)=ω_1 <πχ_{\\mathrm d}(X)=ω_2. \\] A preliminary chain-refinement lemma shows that every inclusion-chain of subsets of a set has a reverse-well-ordered coinitial subchain of controlled cardinality. Thus the result is independent of whether a decreasing local $π$-base is understood as an inclusion-chain, a strictly decreasing transfinite sequence, or a weakly decreasing transfinite sequence. The construction combines a countable star filter, whose centred local $π$-character is at least the pseudointersection number $\\mathfrak p$, with a matrix filter that gives the exact values $ω_1$ and $ω_2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02379",
  "author_total": 1,
  "authors": [
    {
      "name": "Tomasz Kania"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fbnf6cshc41cv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02379",
  "fulltext_url": null,
  "id": "fbnf6cshc41cv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02379",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.02379",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fbnf6cshc41cv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02379",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02379"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Three local $π$-characters",
  "title_text": "Three local π-characters",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/fbnf6cshc41cv",
  "venue": "arXiv",
  "versions": []
}