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

• Main Author: O.R. Sayed
• Format: Article
• Language: English
• Published: SpringerOpen 2012-07-01
• Series: Journal of the Egyptian Mathematical Society
• Subjects: Łukasiewicz logic; Semantics; Fuzzifying topology; α-Irresoluteness; Fuzzifying compactness; α-Compactness
• Online Access: http://www.sciencedirect.com/science/article/pii/S1110256X12000259

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.