{
  "abstract": "In this paper, we introduce a new class of spaces, termed U_c-admitting spaces, and investigate their relationships with U_s-admitting spaces and well-filtered spaces. Adopting the perspective of H-sobriety, we show that every U_c-admitting space is H-sober, so that U_c-admitting spaces arise as a special case of H-sober spaces. Consequently, the category U_c-Sob of U_c-admitting spaces and continuous maps is complete and forms a reflective subcategory of Top_0. In addition, we prove that a T_0 space X is U_c-admitting if and only if its Smyth power space is U_c-admitting. Finally, we present the standard U_c-completion of an arbitrary T_0 space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30967",
  "author_total": 4,
  "authors": [
    {
      "name": "Kangming Lu"
    },
    {
      "name": "Qingguo Li"
    },
    {
      "name": "Shengwen Wang"
    },
    {
      "name": "Rongqi Xiao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/10v5cazk4b9sf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30967",
  "fulltext_url": null,
  "id": "10v5cazk4b9sf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30967",
  "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",
      "cs.LO"
    ],
    [
      "arxiv",
      "math.GN"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7223354339",
  "pdf_url": "https://arxiv.org/pdf/2610.30967",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/10v5cazk4b9sf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30967",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30967"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On U_c-admitting spaces and U_c-completions of T_0 spaces",
  "title_text": "On U_c-admitting spaces and U_c-completions of T_0 spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/10v5cazk4b9sf",
  "venue": "arXiv",
  "versions": []
}