Generalized Topological Structures Induced by H^*-Open Sets and Their Separation Properties

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 (𝕏,τ), the family of all H^*-open subsets of 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.

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BibTeX RIS

BibTeX

@misc{tomar2026generalized,
  title = {{Generalized Topological Structures Induced by $H^*$-Open Sets and Their Separation Properties}},
  author = {Neeraj Kumar Tomar and Komal Priya and Amit Ujlayan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18016},
  eprint = {2610.18016},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18016},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Generalized Topological Structures Induced by H^*-Open Sets and Their Separation Properties
AU  - Neeraj Kumar Tomar
AU  - Komal Priya
AU  - Amit Ujlayan
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18016
UR  - https://arxiv.org/abs/2610.18016
AB  - 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 (𝕏,τ), the family of all H^*-open subsets of 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.
ER  -

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