{
  "abstract": "We give negative answers to two questions of X.Xu concerning the occurrence of the unit interval in nonquasialgebraic quasicontinuous domains. We construct, directly from the binary tree and the binary-value map, a well-founded quasicontinuous dcpo \\[ P=2^{<ω}\\mathbin{\\dot\\cup}[0,1] \\] which is not quasialgebraic. Moreover, $P$ contains no sub-dcpo isomorphic to $[0,1]$, and $[0,1]$ is not a Scott-continuous retract of $P$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20284",
  "author_total": 3,
  "authors": [
    {
      "name": "Chong Shen"
    },
    {
      "name": "Xiaoyong Xi"
    },
    {
      "name": "Dongsheng Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2qaggn6t1mf54.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20284",
  "fulltext_url": null,
  "id": "2qaggn6t1mf54",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20284",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.20284",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2qaggn6t1mf54.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20284",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20284"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Quasicontinuous Domain Without an Interval Retract",
  "title_text": "A Quasicontinuous Domain Without an Interval Retract",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/2qaggn6t1mf54",
  "venue": "arXiv",
  "versions": []
}