Some New Notions of Continuity in Generalized Primal Topological Space

Muhammad Shahbaz, Tayyab Kamran, Umar Ishtiaq (), Mariam Imtiaz, Ioan-Lucian Popa () and Fethi Mohamed Maiz
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Tayyab Kamran: Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan
Umar Ishtiaq: Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54770, Pakistan
Mariam Imtiaz: Department of Mathematics, The Islamia University of Bahawalpur, Bahawalnagar Campus, Bahawalpur 06314, Pakistan
Ioan-Lucian Popa: Department of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania
Fethi Mohamed Maiz: Physics Department, Faculty of Science, King Khalid University, Abha P.O. Box 9004, Saudi Arabia

Mathematics, 2024, vol. 12, issue 24, 1-23

Abstract: This study analyzes the characteristics and functioning of S g ∗ -functions, S g ∗ -homeomorphisms, and S g ∗ # -homeomorphisms in generalized topological spaces ( GTS ) . A few important points to emphasize are S g ∗ -continuous functions, S g ∗ -irresolute functions, perfectly S g ∗ -continuous, and strongly S g ∗ -continuous functions in GTS and generalized primal topological spaces ( GPTS ) . Some specific kinds of S g ∗ functions, such as S g ∗ -open mappings and S g ∗ -closed mappings, are discussed. We also analyze the GPTS , providing a thorough look at the way these functions work in this specific context. The goal here is to emphasize the concrete implications of S g ∗ functions and to further the theoretical understanding of them by merging different viewpoints. This work advances the area of topological research by providing new perspectives on the behavior of S g ∗ functions and their applicability in various topological settings. The outcomes reported here contribute to our theoretical understanding and establish a foundation for further research.

Keywords: generalized primal topological space; ? g – S g ? -continuous function; ? g – S g ? -homeomorphism; ? g – S g ? # -homeomorphism; P g – S g ? -continuous function; P g – S g ? -homeomorphism; P g – S g ? # -homeomorphism (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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