{
  "abstract": "We give negative answers to Questions 4.4 and 4.5 in Cao's survey on the Wijsman topology. We construct a metrizable space $Y$ and a compatible metric $d$ such that every finite power $Y^n$ is Baire, while $(\\mathrm{CL}(Y),τ_W(d))$ is not Baire. The construction realizes the Vietoris hyperspace of a suitable metric space as an open subspace of a ball hyperspace. We also study the set $S_d$ of points having an open $σ$-$d$-totally bounded neighborhood. We prove that Baireness of $(\\mathrm{CL}(X),τ_W(d))$ implies Baireness of $S_d$, and that, whenever $S_d$ is dense in $X$, the following three conditions are equivalent: $(\\mathrm{CL}(X),τ_W(d))$ is Baire, $X$ is Baire, and $S_d$ is Baire. As consequences, we obtain complete characterizations for locally $σ$-$d$-totally bounded metric spaces, countable metric spaces, and $σ$-compact metrizable spaces. In our counterexample, $S_e$ coincides with a non-dense discrete component for every compatible metric $e$, showing that the density assumption is essential.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35921",
  "author_total": 1,
  "authors": [
    {
      "name": "Basile Beyer de Ryke"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7zh9s8ayyjjmp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35921",
  "fulltext_url": null,
  "id": "7zh9s8ayyjjmp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35921",
  "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.GM"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7224081919",
  "pdf_url": "https://arxiv.org/pdf/2610.35921",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7zh9s8ayyjjmp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.35921",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35921"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Advanced Topology and Set Theory",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On Baireness of the Wijsman Topology",
  "title_text": "On Baireness of the Wijsman Topology",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/7zh9s8ayyjjmp",
  "venue": "arXiv",
  "versions": []
}