Some New Notions of Continuity in Generalized Primal Topological Space

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.