{
  "abstract": "We establish the cardinal inequality \\(|X|\\leq 2^{t(X)Hψ(X)}\\) for every Hausdorff SDL space \\(X\\), where \\(t(X)\\) and \\(Hψ(X)\\) denote the tightness and the Hausdorff pseudocharacter of \\(X\\), respectively. Since both invariants are bounded by \\(χ(X)\\), this yields \\(|X|\\leq 2^{χ(X)}\\). As a consequence, every first-countable Hausdorff strongly cellular--Lindelöf space has cardinality at most the continuum. These results answer Questions~2.1 and~2.2 of Bella and Spadaro. An intermediate result is a uniform bounded-decomposition property for SDL spaces; in particular, their strict quasi--Lindelöf number satisfies \\(\\sqL(X)\\leq t(X)\\).",
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  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00599",
  "author_total": 2,
  "authors": [
    {
      "name": "Gabriel Fernandes"
    },
    {
      "name": "João Marcelo Maciel Messias"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2q5a4bhxtc6gs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00599",
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  "id": "2q5a4bhxtc6gs",
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  "landing_url": "https://arxiv.org/abs/2609.00599",
  "language": null,
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GN"
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      "arxiv",
      "math.LO"
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      "openalex",
      "2608|Advanced Topology and Set Theory"
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  "pdf_url": "https://arxiv.org/pdf/2609.00599",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2q5a4bhxtc6gs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.00599",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00599"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Cardinality Bounds for Hausdorff SDL Spaces",
  "title_text": "Cardinality Bounds for Hausdorff SDL Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/2q5a4bhxtc6gs",
  "venue": "arXiv",
  "versions": []
}