{
  "abstract": "We completely resolve Question~5.3 of Kania's paper \\cite{Kania} and establish a more general realization theorem. We show that for infinite cardinals $μ\\leqslantν<κ<λ$, a space with \\[ \\pc(X)=μ,\\qquad\\pcl(X)=ν,\\qquad \\pcc(X)=κ,\\qquad\\pcd(X)=λ\\] exists if and only if $κ\\leqslant2^μ$. The witnesses may be zero-dimensional and Tychonoff spaces, of the least possible cardinality $λ$. They may have the least possible number of non-isolated points, or alternatively be crowded. The main ingredient is an exact computation of the centered local $π$-character of star filter spaces in terms of ultrafilter character, obtained from a finite selection lemma for filter pushforwards. We also construct a single space with countable $r$-linked local $π$-bases for every finite $r$, centered value $ω_1$, and any prescribed decreasing value greater than $ω_1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12612",
  "author_total": 1,
  "authors": [
    {
      "name": "Jerzy Kcakol"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2dqtkbgq6sp98.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12612",
  "fulltext_url": null,
  "id": "2dqtkbgq6sp98",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12612",
  "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.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7221511712",
  "pdf_url": "https://arxiv.org/pdf/2610.12612",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2dqtkbgq6sp98.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12612",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12612"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Ultrafilter characters and local $π$-bases",
  "title_text": "Ultrafilter characters and local π-bases",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/2dqtkbgq6sp98",
  "venue": "arXiv",
  "versions": []
}