Gradations of openness and Chang’s fuzzy topologies

Abstract

We study some properties of gradations of openness defined on a set X and prove that each gradation of openness δ is the supremum (infimum) of a strictly increasing (decreasing) sequence of gradations of openness which are equivalent to δ. Also, we characterize those fuzzy topological spaces (X, T) with the property that there exists a gradation of openness σ from I X onto I such that G∈ T iff σ(G)>0.