Some New Notions of Continuity in Generalized Primal Topological Space

This study analyzes the characteristics and functioning of Sg∗-functions, Sg∗-homeomorphisms, and Sg∗#-homeomorphisms in generalized topological spaces (GTS). A few important points to emphasize are Sg∗-continuous functions, Sg∗-irresolute functions, perfectly Sg∗-continuous, and strongly Sg∗-continuous functions in GTS and generalized primal topological spaces (GPTS). Some specific kinds of Sg∗ functions, such as Sg∗-open mappings and Sg∗-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 Sg∗ 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 Sg∗ functions and their applicability in various topological settings. The outcomes reported here contribute to our theoretical understanding and establish a foundation for further research.