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Unifying Concepts in Topology: Analyzing Sg∗-Open and Sg∗-Closed Sets in Generalized Primal Topological Spaces

Author

Listed:
  • Muhammad Shahbaz
  • Tayyab Kamran
  • Mariam Imtiaz
  • Umar Ishtiaq
  • Ioan-Lucian Popa

Abstract

This research introduces the concept of Sg∗-open and Sg∗-closed sets within the framework of primal topological spaces, extending the existing body of knowledge in topology. Initially, this paper reviews fundamental topological structures, including open sets, semiopen sets, semistar open sets, and generalized open sets in generalized topological spaces GTSs. Subsequently, we systematically integrate these concepts into generalized primal topological spaces GPTSs, leading to novel insights and relationships within this mathematical structure. A comparative analysis of GTS and GPTS highlights their key differences and interconnections, enriching the understanding of these spaces. Finally, this study opens new pathways for future topological research by further incorporating open set concepts into GPTS.

Suggested Citation

  • Muhammad Shahbaz & Tayyab Kamran & Mariam Imtiaz & Umar Ishtiaq & Ioan-Lucian Popa, 2026. "Unifying Concepts in Topology: Analyzing Sg∗-Open and Sg∗-Closed Sets in Generalized Primal Topological Spaces," Journal of Mathematics, Hindawi, vol. 2026, pages 1-17, January.
    • Handle: RePEc:hin:jjmath:5674463
    DOI: 10.1155/jom/5674463
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