Fuzzy almost continuity and its pointwise characterization by dual points and fuzzy nets

Abstract We introduce the notions of fuzzy almost continuity and fuzzy weak continuity at a fuzzy point. Following the pointwise approach, we investigate their fuzzy topological properties. We also obtain a pointwise characterization of fuzzy almost continuous functions by dual points and fuzzy nets. The main idea behind this work is to establish a local theory in the study of continuity and its weaker forms in general fuzzy topological spaces.