Exploring g*b-Compactness and g*b-Connectedness through Generalized Topologies with Applications

Vidhya; Saied Jafari; Shobana A; Logapriya B

doi:10.5269/bspm.78607

Vidhya Professor, Department of Science and Humanities(Mathematics), Karpagam Institute of Technology, Coimbatore
Saied Jafari Dr. Rer. Nat. in Mathematics, Professor, College of Vestsjaelland South: Slagelse, Vestsjaelland Syd, DK https://orcid.org/0000-0001-5744-7354
Shobana A Professor, Department of Science and Humanities, Nehru Institute of Technology
Logapriya B

Résumé

This paper presents and explores two extended topological structures g*b-compactness and g*b-connectedness which serve as generalizations of classical compactness and connectedness by incorporating the concepts of g-open and b-open sets. Beyond their theoretical significance, these generalized spaces offer valuable tools for modeling and analyzing complex systems where classical topological assumptions may not hold. Potential applications include the design of resilient network topologies, analysis of digital images and data clusters, control systems in engineering, and non-standard models in theoretical physics. The characteristics of c g*b-ompact and g*b-connected spaces examined in this study establish a strong foundation for advancing topological analysis in contexts where generalized notions of openness and continuity are fundamental.

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