New Topological Group Construction via *h- Set
Abstract
This paper introduces the class of *h - topological groups, applying *h -continuous group operations. We establish several basic properties and characterizations that distinguish them from classical topological groups. A collection of examples is provided to illustrate these differences and to demonstrate the scope of the framework. Also we define *h - irresolute topological groups and investigate their connection with *h - topological groups, proving that every *h - irresolute topological group is *h - topological, whereas the converse does not generally hold. Collectively, these results extend the framework of generalized topologies and offer a broader foundation for analyzing algebraic structures equipped with non-standard
notions of openness.
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References
[2] Dunham.W, A new closure operator for Non- T1 toplogies, kyungpook Math.J, 22(1) (1982), 55-60.
[3] Levine.N, Generatized closed sets in Topology, Rend. Circ. Mat. Palermo, 19(2)(1970), 89-89.
[4] Pontryagin.L. S, Topological Groups, 2nd ed., Gordon and Breach Taylor and Francis, New York London Paris, (1986).
[5] Shyamala.G.R, Meera Devi.B, *h - Open Sets in Topological Spaces, Proceedings of International Conference on Recent Advances in Algebra, ISBN; 978-93-341-2459-0, (2024), 74-78.
[6] Shyamala.G.R, Meera Devi.B, New Class of Mappings Via *h - Set, Proceedings of International Conference on Recent Trends in Applied Mathematics and Computer Science, ISBN; 978-81-974481-3-3, (2025), 264-268.
[7] Tkachenko.M, Paratopological and semitopological groups vs topological groups, Recent Progress in General Toplogy III, Atlantis Press,
(2014), 825-882.
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