{
  "abstract": "In this paper, we focus on the sobriety of the Scott topology in countable case. Specifically, we show that: (1) every meet-continuous core-compact countable dcpo is sober with respect to the Scott topology; (2)every countable locally compact dcpo is sober endowed with the Scott topology; (3) the lattice of all open sets for the rational numbers space Q equipped with the Scott topology is not sober.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24001",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhengmao He"
    },
    {
      "name": "Zhaochen Dong"
    },
    {
      "name": "Kaiyun Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/47w2jp8t75bjb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24001",
  "fulltext_url": null,
  "id": "47w2jp8t75bjb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24001",
  "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",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7214015854",
  "pdf_url": "https://arxiv.org/pdf/2609.24001",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/47w2jp8t75bjb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.24001",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24001"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Sobriety of Scott topologies under countability conditions",
  "title_text": "Sobriety of Scott topologies under countability conditions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/47w2jp8t75bjb",
  "venue": "arXiv",
  "versions": []
}