{
  "abstract": "Lawson and Mislove posed the following problem in 1990 as Problem~535 in \\emph{Open Problems in Topology}: for a core-compact space \\(X\\) and a dcpo \\(P\\) equipped with its Scott topology, under what conditions on \\(P\\) do the Isbell and Scott topologies on \\(C(X,P)\\) agree?It was proved that, for a nonempty bicomplete continuous dcpo \\(P\\), the Isbell and Scott topologies on \\(C(X,P)\\) coincide for every core-compact space \\(X\\) if and only if \\(P\\) is bounded complete; for every compact core-compact space \\(X\\) if and only if \\(P\\) is conditionally bounded complete; and for every RW-space \\(X\\) if and only if \\(P\\) is a pointed continuous \\(L\\)-domain.We remove the bicompleteness assumption from all three classifications by combining the forbidden-retract theorem of Jia, Jung and Li with a separation theorem for powers of downward well-ordered chains and suitable Alexandrov test spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28123",
  "author_total": 3,
  "authors": [
    {
      "name": "Yuxu Chen"
    },
    {
      "name": "Yunjie Wen"
    },
    {
      "name": "Xiaoyong Xi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/amsb0vq0g082b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28123",
  "fulltext_url": null,
  "id": "amsb0vq0g082b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28123",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GN"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7214160596",
  "pdf_url": "https://arxiv.org/pdf/2609.28123",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/amsb0vq0g082b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28123",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28123"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Scott--Isbell Coincidence for Continuous Dcpos beyond Bicompleteness",
  "title_text": "Scott--Isbell Coincidence for Continuous Dcpos beyond Bicompleteness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/amsb0vq0g082b",
  "venue": "arXiv",
  "versions": []
}