TAILIEUCHUNG - C-closed sets in L-fuzzy topological spaces and some of its applications

We introduce and study the notion of C–closed sets in L–fuzzy topological spaces. Then, C–convergence theory for nets and ideals is established in terms of C–closedness. Finally, we give a new concept of C–continuity on L–fuzzy topological space by means of L–fuzzy C–closedness and investigate some of its properties and its relationships with other L–fuzzy mappings introduced previously. Then we systematically study the characterizations of this notion with the aid of the C–convergence of L–fuzzy nets and L–fuzzy ideals. | Turk J Math 26 (2002) , 245 – 261. ¨ ITAK ˙ c TUB C–Closed Sets in L–Fuzzy Topological Spaces and Some of its Applications Ali Ahmed Nouh Abstract We introduce and study the notion of C–closed sets in L–fuzzy topological spaces. Then, C–convergence theory for nets and ideals is established in terms of C–closedness. Finally, we give a new concept of C–continuity on L–fuzzy topological space by means of L–fuzzy C–closedness and investigate some of its properties and its relationships with other L–fuzzy mappings introduced previously. Then we systematically study the characterizations of this notion with the aid of the C–convergence of L–fuzzy nets and L–fuzzy ideals. Keywords and phrases. L–fuzzy topology, Qα –compactness, L–fuzzy C–closed set, L–fuzzy C–continuous mappings, L–fuzzy net, L–fuzzy ideal, C–convergence. 1. Introduction Continuity and its weaker forms constitute an important and intensely investigated area in the field of general topological spaces. For example, the notions of almost continuous, N–continuous, H–continuous, C–continuous, weakly continuous and semi– continuous have been introduced by different authors, and their inter–relationships with other topological notions have been established. Most of these notions turn out to be local properties; hence the pointwise approach is generally preferred in their studies and definitions. The concept of C–continuity in general topology was introduced by Gentry and Hoyle [5] in 1970. The class of C–closed sets (compact and closed) was defined by Garg and Kumar [4] in 1989. Then several characterizations of C–continuous mappings in terms of C–closed sets are given. Recently, Dang, Behera and Nanda [3] extended the concept to fuzzy topology, and introduced the notion of fuzzy C–continuous function using the fuzzy compactness given by Mukherjee and Sinha [8]. However, the fuzzy compactness has some shortcomings, such as the Tychonoff product theorem does not AMS Subject Classification 2000 : 54A20, .

• Toán học
• L fuzzy topology
• Qα compactness
• L fuzzy C closed set
• L fuzzy C continuous mappings
• L fuzzy net
• L fuzzy ideal
• C convergence