A Unified Theory on Some Basic Topological Concepts

Abstract

Several mathematicians, including myself, have studied some unifications in general topological spaces as well as in fuzzy topological spaces. For instance in our earlier works, using operations on topological spaces, we have tried to unify some concepts similar to continuity, openness, closedness of functions, compactness, filter convergence, closedness of graphs, countable compactness and Lindelof property. In this article, to obtain further unifications, we will study $\phi_{1,2}$-compactness and relations between $\phi_{1,2}$-compactness, filters and $\phi_{1,2}$% -closure operator.