{
  "abstract": "We prove that a domain $D$ is an RB-domain if and only if the function space $[D\\to E]$ is continuous for every domain $E$, thereby resolving a conjecture of Luan and Li. More precisely, for each domain $D$ we construct an explicit algebraic test domain $A_D$ such that continuity of the single function space $[D\\to A_D]$ already forces $D$ to be an RB-domain. For countably based domains $D$, the test domain can be chosen as a fixed domain that is independent of $D$. The analogous continuity characterization of FS-domains is false: the closed-disk domain is an FS-domain, but its function space into a suitable pointed algebraic domain is not continuous.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20187",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuxu Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b5j07w5y5jgag.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20187",
  "fulltext_url": null,
  "id": "b5j07w5y5jgag",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20187",
  "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",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7213612184",
  "pdf_url": "https://arxiv.org/pdf/2609.20187",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b5j07w5y5jgag.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20187",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20187"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A function space characterization of RB-domains",
  "title_text": "A function space characterization of RB-domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/b5j07w5y5jgag",
  "venue": "arXiv",
  "versions": []
}