On separation axioms in fuzzifying generalized topology

Abstract

Abstract. In this paper we introduce and study the concept of fuzzifying separation axioms in fuzzifying generalized topological spaces.

Separation axioms in \(L\)-fuzzifying supra-topology

“…Since the complete residuated lattice I = [0, 1] as defined in [10,11] satisfies all the conditions in our work, then our results are generalizations of the corresponding results in [2] as we illustrate through this paper.…”

“…Sometimes we need more conditions on L such as the completely distributive law or that the " ∧ " is distributive over arbitrary joins or the double negation law as we illustrate through this paper. As applications of our work the corresponding results (see [2,13]) are generalized and new consequences are obtained.…”

“…In fuzzifying topology, separation axioms were introduced and studied in [6,9,10]. Also, Gowrisankar et al [2] introduced the concepts of T 0 -, T 1 -, T 2 (Hausdorff)-, T 3 (regularity)-, T 4 (normality)-, R 0 -, and R 1 -separation axioms in fuzzifying supra-topology. is gave in L-fuzzifying supra-topology where L is a complete residuated lattice.…”