(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this research, we introduce and analyze the concepts of \(G\)-compactness, \(G\)-Lindelofness, and \(G\)-countably compactness within the framework of topological spaces, which are characterized by more rigorous conditions compared to those governing compact and Lindelof spaces. We formulate a series of theorems and present a variety of examples to clarify the relationships among \(G\)-compactness, \(G\)-Lindelofness, compactness, and Lindelofness. Additionally, we define the \(G\)-separation axioms utilizing G_δ sets and explore the interrelations among these concepts.