A thesis submitted in partial fulfillment of the requirements for the degree of master in mathematics

Abstract

The closed graph theorem is one of the deeper results in the theory of Banach spaces and one of the richest in its applications to functional analysis. Under what conditions will a closed linear operator be bounded? An answer is given by closed graph theorem. We present Closed Graph and Open Mapping theorems for bounded linear operators acting between Banach and topological spaces. We give definitions and examples of different spaces, bounded linear operators and functionals on this spaces, and we give applications of the previous theorems to Closed Graph and Open Mapping Theorems as well as the Uniform Bounded Principle and Baire Category Theorem.