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Browsing Mathematics by Author "Dr. Fawwaz Abudiak"
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- ItemExtending Topological Properties to Fuzzy Topological Space(2014) Ruba Mohammad Abdul-Fattah Adarbeh; Dr. Fawwaz AbudiakIn 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.
- ItemTopological Characters of Complete Metric Spaces(2015) Haneen Akram Mustafa Ghanim; Dr. Fawwaz AbudiakIn this thesis the topological aspects of complete metric spaces are studied. Complete metric spaces, Characterizations of complete metric spaces and examples of complete metric spaces are presented. A completion of a metric space is discussed. Function spaces and their topologies are defined and studied. Completeness of function spaces is considered. As an application, a construction of the well-known Peano space –filling curve is discussed. Finally, Theorems of topological characters concerning complete spaces such as Heine-Borel theorem, Ascoli's theorem and Baire's theorem with their proofs are introduced, in addition to other matters concerning the subject. The existence of continuous nowhere-differentiable real-valued functions is proved.