G-Compact Spaces Characterized by the Intersection of Countable Neighborhoods (European Journal of Pure and Applied Mathematics, 2025)
In this research, we introduce and analyze the concepts of \(G\)-compactness, \(G\)-Lindel$\ddot{o}$fness, and \(G\)-countably compactness within the framework of topological spaces, which are characterized by more rigorous conditions compared to those governing compact and Lindel$\ddot{o}$f spaces. We formulate a series of theorems and present a variety of examples to clarify the relationships among \(G\)-compactness, \(G\)-Lindel$\ddot{o}$fness, compactness, and Lindel$\ddot{o}$fness. Additionally, we define the \(G\)-separation axioms utilizing $G_δ$ sets and explore the interrelations among these concepts.
Keywords: compact space; Lindel$\ddot{o}$f space; countably compact space; G-compact space; G-Lindel$\ddot{o}$f space; G-countably compact; separation axioms; G-separation axioms