{
  "abstract": "In this paper, we obtain two complete lattices that are sober with respect to the Scott topology, whereas the Scott space of their product is not a sober space. Thus, we answer a question posed by Miao, Xi, Jia, Li and Zhao in [8].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39246",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhengmao He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eejbrw9cwyrgg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39246",
  "fulltext_url": null,
  "id": "eejbrw9cwyrgg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39246",
  "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",
      "1703|Advanced Algebra and Logic"
    ]
  ],
  "openalex": "W7216595971",
  "pdf_url": "https://arxiv.org/pdf/2609.39246",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eejbrw9cwyrgg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2609.39246",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39246"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The product of two Scott sober complete lattices is not always Scott sober",
  "title_text": "The product of two Scott sober complete lattices is not always Scott sober",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/eejbrw9cwyrgg",
  "venue": "arXiv",
  "versions": []
}