Almost separation axioms in fuzzifying topology

Abstract

In the present paper, we introduced topological notions defined by means of regular open sets  when these are planted into the framework of Ying's fuzzifying topological spaces (in Lukasiewicz fuzzy logic). We used fuzzy logic to introduce almost separation  axioms \(T_{0}^{R}\)-, \(T_{1}^{R}\)-, \(T_{2}^{R}\) (almost Hausdorff)-, \(T_{3}^{R}\) (almost-regular)- and \(T_{4}^{R}\) (almost-normal). Furthermore, the \(R_{0}^{R}\)- and \(R_{1}^{R}\)-separation axioms  have been studied and their relations with the \(T_{1}^{R}\)- and \(T_{2}^{R}\)-separation axioms have been introduced. Moreover, we gave the relations of these axioms with each other as  well as the relations with other fuzzifying separation axioms.