INTRODUCTION TO METRIC SPACES, intended as a textbook fulfilling the NEP and UGCF 2022 requirements, is designed for the third and fourth year undergraduate students. Various concepts and applications, examples and results in the book are explained in an easy and friendly way for undergraduates to understand the importance and usefulness of metric spaces. The text begins with a preliminary chapter to recall notations, definitions and results from calculus and analysis, followed by an introduction and discussion on metric spaces together with open sets, closed sets etc. Sequences, completeness, separable sets, dense sets and the Baire Category Theorem are studied in the third chapter. Continuous functions, homeomorphisms and concepts like Banach Fixed Point Theorem are discussed in the subsequent chapter. Connectedness and compactness of metric spaces are dealt with in the fifth chapter and the sixth chapter, respectively. As a generalization and an extension of metric spaces, the last chapter gives a glimpse of topological spaces, normed spaces and inner product spaces. Various concepts of metric spaces and related spaces are supplemented with suitable graphical representations in the text.

• • Several examples with explanation • Geometrical illustrations • Relevant practice exercises • Excellent for self-study

Preface / Acknowledgement / Preliminaries / Metric Spaces / Sequences and Completeness / Continuous Functions and Homeomorphisms / Connectedness / Compactness / Introduction to Topological and Normed Spaces / Bibliography / Index.

Undergraduate and Graduate Students, Professionals & Researchers