{
  "abstract": "In this paper, we investigate how the properties of the nowhere dense subspaces reflect those of the entire space. We call a space X an SAC-P space if the set of accumulation points of any infinite family of mutually disjoint open subsets of X is a non-empty set having property P. We prove that for a regular space X, X is SAC-compact precisely when it is compact. In general, for a regular space X, X is SAC-P (here, P is a property which closed subsets inherit) exactly when X is feebly compact and each closed nowhere dense subspace of X has property P. Similar to discrete reflexivity, we introduce the notion of nowhere dense reflexivity. A property P is nowhere densely reflexive inA if each space X∈A has property P precisely when each closed nowhere dense subspace of X has property P. We prove that compactness, linear Lindelöfness and initial κ-compactness are all nowhere densely reflexive both in the class of feebly compact spaces and in that of dense-in-itself spaces. For topological groups, we prove that if G is a non-compact connected feathered topological group, then G is metrizable precisely when each closed nowhere dense subgroup of G is metrizable.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Basic Courses, Suzhou City University, Suzhou 215104, China",
    "School of Mathematics, Nanjing University, Nanjing 210093, China",
    "School of Mathematics, Nanjing Audit University, Nanjing 211815, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Dong-Fang Xie"
    },
    {
      "affs": [
        1
      ],
      "name": "Wei-Xue Shi"
    },
    {
      "affs": [
        2
      ],
      "name": "Wei-Feng Xuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bc9qxqthgda2f.bib",
  "cited_by": 0,
  "doi": "10.3390/axioms15100736",
  "fulltext_url": null,
  "id": "bc9qxqthgda2f",
  "issns": [
    "2075-1680"
  ],
  "landing_url": "https://www.mdpi.com/2075-1680/15/10/736",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7216036663",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/bc9qxqthgda2f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:30Z",
      "native_id": "10.3390/axioms15100736",
      "source": "crossref",
      "url": "https://www.mdpi.com/2075-1680/15/10/736"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Advanced Topology and Set Theory",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On SAC-P Spaces and Nowhere Densely Reflexive Properties",
  "title_text": "On SAC-P Spaces and Nowhere Densely Reflexive Properties",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:30Z",
  "url": "https://research.draconitic.com/paper/bc9qxqthgda2f",
  "venue": "Axioms",
  "versions": []
}