(untitled) (European Journal of Pure and Applied Mathematics, 2025)
The principal aims of this paper include the introduction of the concept of σ-compact Spaces in n^th-topological spaces, the definition of compactness, discussion of various generalizations encompassing compactness in n^th-topological space, the properties of σ-compact Spaces. Furthermore, our study extends to the analysis of the notion of countable compactness in n^th-topological spaces. Our investigation extends to various generalizations of these spaces.