An-Najah Staff

In this thesis the topological properties of fuzzy topological spaces were investigated and have been associated with their duals in classical topological spaces. Fuzzy sets, fuzzy functions and fuzzy relations were presented along with their properties. Different types of fuzzy topological spaces (FTS) were introduced in Chang’s and Lowen’s sense as well as intuitionistic (FTS). Many topological properties were proved to be extensions to those in non fuzzy setting, while examples were presented for those non extension properties. For instance, the closure of the product is not equal to the product of the closures. Also different approaches of separation axioms were investigated using Q-neighborhoods and fuzzy points, it turns out that most of them are not extension of classical separation axioms. Fuzzy topological properties are considered, for instance, we studied fuzzy connectedness and fuzzy compactness. It is found that the product of an infinite number of fuzzy compact spaces may not be compact. Finally, fuzzy continuity, fuzzy almost continuity and fuzzy ??-continuity were introduced with a theorem proved the way they are related.