Discussion Committee:
Dr. Fawwaz Abudiak / Supervisor
Dr. Bassam Manasrah/ External Examiner
Dr. Mohammad ALamlah / Internal Examiner
Supervisors:
Dr. Fawwaz Abudiak / Supervisor
Authors:
Haneen Akram Mustafa Ghanim
Abstract:
In 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.