{
  "abstract": "In 1974, C. D. Aliprantis posed several questions concerning topological completions of locally solid vector lattices. We answer all of them in the negative. We construct Hausdorff locally convex-solid vector lattices showing that, without metrizability, neither the $σ$-Lebesgue property nor property (B, i) need pass to the completion; a positive element of the completion need not be the limit of a decreasing sequence of upper elements; the generalized (A, 0) property need not make the canonical image a regular sublattice; and regularity of this image need not imply order density. All five counterexamples have been formalized in Lean 4 using the Banach lattice Lean library.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29498",
  "author_total": 3,
  "authors": [
    {
      "name": "David Muñoz-Lahoz"
    },
    {
      "name": "Mitchell A. Taylor"
    },
    {
      "name": "Pedro Tradacete"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8f315cx6kemgh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29498",
  "fulltext_url": null,
  "id": "8f315cx6kemgh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29498",
  "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.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7214331140",
  "pdf_url": "https://arxiv.org/pdf/2609.29498",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8f315cx6kemgh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29498",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29498"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Aliprantis's questions on locally solid topologies",
  "title_text": "Aliprantis's questions on locally solid topologies",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/8f315cx6kemgh",
  "venue": "arXiv",
  "versions": []
}