Functional Analysis with Applications

The author presents the essentials of functional analysis and discusses basic metric and topological concepts. Four fundamental theorems are presented - Functional Analysis-Hahn- Banach Theorem, Open Mapping Theorem, Closed Graph Theorem, and Banach-Steinhaus Theorem, and basic results on operators in Banach and Hilbert spaces and Spectral theory are also included. There are numerous exercises. About the Book: This book provides exposition of the subject both in its general and algebraic aspects. It deals with the notions of topological spaces, compactness, connectedness, completeness including metrizability and compactification, algebraic aspects of topological spaces through homotopy groups and homology groups. It begins with the basic notions of topological spaces but soon going beyond them reaches the domain of algebra through the notions of homotopy, homology and cohomology. How these approaches work in harmony is the subject matter of this book. The book finally arrives at the Intended as a textbook for a course on Functional Analysis, this title can also be useful for scientists and engineers. It features proofs and motivation for the theory and applications; keeping in view the importance of the subject Operator theory and Fixed point theory.