{
  "abstract": "Strong well-filteredness is a refinement of well-filteredness arising naturally in non-Hausdorff topology and domain theory. In this paper, we construct a countable locally compact strong R-space X such that neither its Smyth power space nor its Scott power space is a strong d-space. This example gives negative answers to the questions concerning the preservation of strong well-filteredness and the strong R-space property under power space constructions. Furthermore, for the two-point discrete space \\two, the function space (\\two,X) is not a strong d-space under any of the pointwise convergence, compact-open, Isbell, core-open or Scott topologies, where the Scott topology is induced by the pointwise order.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02725",
  "author_total": 4,
  "authors": [
    {
      "name": "Zhenzhu Yuan"
    },
    {
      "name": "Xiangrui Li"
    },
    {
      "name": "Bei Liu"
    },
    {
      "name": "Qinggguo Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0vd87n44bvay8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02725",
  "fulltext_url": null,
  "id": "0vd87n44bvay8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02725",
  "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",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7220413894",
  "pdf_url": "https://arxiv.org/pdf/2610.02725",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0vd87n44bvay8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02725",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02725"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A note on power spaces and function spaces of strongly well-filtered spaces",
  "title_text": "A note on power spaces and function spaces of strongly well-filtered spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/0vd87n44bvay8",
  "venue": "arXiv",
  "versions": []
}