{
  "abstract": "In this paper, we investigate the family of $H^{*}$-open sets from the perspective of generalized topology and examine the structural and separation properties arising from it. For a topological space $(\\mathbb{X},τ)$, the family of all $H^{*}$-open subsets of $\\mathbb{X}$ is considered as a natural candidate for an $H^{*}$-generated generalized topology. We establish conditions under which this family forms a strong generalized topology and identify additional assumptions that allow the resulting structure to be treated as an ordinary topology. This distinction provides a systematic framework for studying $H^{*}$-open sets without imposing finite-intersection properties in advance. Within this framework, we investigate the corresponding $H^{*}$-interior and $H^{*}$-closure operators and analyze separation properties determined by the $H^{*}$-open structure. When the $H^{*}$-generated family forms a topology, the resulting associated space is used to relate generalized $H^{*}$-separation properties to their classical topological counterparts. We further examine compactness-type properties, subspace behaviour, and preservation under suitable mappings. Examples are included to illustrate how the structure generated by $H^{*}$-open sets may exhibit separation behaviour different from that of the original topology. The results provide a unified setting for connecting $H^{*}$-open-set theory with generalized topological structures and offer a basis for further investigation of separation and covering properties in this framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18016",
  "author_total": 3,
  "authors": [
    {
      "name": "Neeraj Kumar Tomar"
    },
    {
      "name": "Komal Priya"
    },
    {
      "name": "Amit Ujlayan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0bg3qmvmc5282.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18016",
  "fulltext_url": null,
  "id": "0bg3qmvmc5282",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18016",
  "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",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7221835033",
  "pdf_url": "https://arxiv.org/pdf/2610.18016",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0bg3qmvmc5282.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.18016",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18016"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Generalized Topological Structures Induced by $H^{*}$-Open Sets and Their Separation Properties",
  "title_text": "Generalized Topological Structures Induced by H^*-Open Sets and Their Separation Properties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/0bg3qmvmc5282",
  "venue": "arXiv",
  "versions": []
}