{
  "abstract": "Given a subset system $H$ on $T_0$-spaces, we associate with each topology a closure-testing derived topology and study the fixed points of this operator. The $H$-determined topologies above a given topology are closed under intersections and hence determine a least fixed-point hull. We prove that this hull is obtained by transfinite iteration, is functorial, and defines a right adjoint to the inclusion of $H$-determined spaces into $\\mathbf{Top}_0$. Consequently, the corresponding full subcategory is coreflective and complete. We isolate restriction-stability and open-locality hypotheses under which determinedness is inherited by closed and open subspaces, and we establish a general non-reflectivity criterion. If $H$ is contained in the directed-subset system, the category of $H$-determined spaces is Cartesian closed; its exponentials are obtained by coreflecting the pointwise convergence topology on continuous maps. The construction subsumes familiar monotone- and irreducible-determined cases while separating the formal consequences of the subset-system axioms from the additional hypotheses needed for heredity and exponentials. It therefore provides a uniform categorical mechanism for producing complete Cartesian closed categories of $T_0$-spaces with explicit higher-order function spaces, as required in denotational semantics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01698",
  "author_total": 3,
  "authors": [
    {
      "name": "Xiaoquan Xu"
    },
    {
      "name": "Xinjie Huang"
    },
    {
      "name": "Yi Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8v877tnxqefte.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01698",
  "fulltext_url": null,
  "id": "8v877tnxqefte",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01698",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GN"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01698",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8v877tnxqefte.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01698",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01698"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Subset-system derived topologies and coreflective categories of $T_0$-spaces",
  "title_text": "Subset-system derived topologies and coreflective categories of T_0-spaces",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/8v877tnxqefte",
  "venue": "arXiv",
  "versions": []
}