α-Irresoluteness and α-compactness based on continuous valued logic

Abstract

Abstract This paper considers fuzzifying topologies, a special case of I -fuzzy topologies (bifuzzy topologies), introduced by Ying [1] . It investigates topological notions defined by means of α -open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Łukasiewicz logic in [0, 1]) . The concept of α -irresolute functions and α -compactness in the framework of fuzzifying topology are introduced and some of their properties are obtained. We use the finite intersection property to give a characterization of fuzzifying α -compact spaces. Furthermore, we study the image of fuzzifying α -compact spaces under fuzzifying α -continuity and fuzzifying α -irresolute maps.