{
  "abstract": "Let \\(H(A)\\) be the Hattori space associated with \\(A\\subseteq\\mathbb R\\), and put \\(B=\\mathbb R\\setminus A\\). Kulesza announced at the 2018 Joint Mathematics Meetings that Lindelöfness of \\(H(A)^{2n}\\) forces Lindelöfness of \\(H(A)^{2n+1}\\) for every positive integer \\(n\\). The meeting abstract states this implication without a proof. This paper proves the case \\(n=1\\) in ZFC. The same one-sided geometry gives a pointwise half-space criterion for affine discreteness and, when \\(H(A)^2\\) is Lindelöf, a four-coordinate obstruction for uncountable closed discrete monotone traces. Known results on mixed Sorgenfrey--Euclidean products lead to hereditary-Lindelöf criteria for finite powers, a countable-power characterization, and a finite-power Lindelöf reduction. A transfinite construction gives \\(A\\subseteq\\mathbb R\\) for which \\(H(A)^2\\) and \\(H(A)^3\\) are Lindelöf, whereas \\(H(A)^4\\) contains a closed discrete affine line of cardinality \\(\\mathfrak c\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00853",
  "author_total": 1,
  "authors": [
    {
      "name": "Xing-Yu Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c244r8jhmbt3x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00853",
  "fulltext_url": null,
  "id": "c244r8jhmbt3x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00853",
  "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.GN"
    ],
    [
      "arxiv",
      "math.LO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.00853",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c244r8jhmbt3x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00853",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00853"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Square-to-Cube Lindelöfness and Power Separations in Hattori Spaces",
  "title_text": "Square-to-Cube Lindelöfness and Power Separations in Hattori Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/c244r8jhmbt3x",
  "venue": "arXiv",
  "versions": []
}