INTRODUCTION TO METRIC SPACES

The book is based on a course of lectures given at the University of Easte Anglia and is written in an easily understood style for undergraduates who have completed elementary analysis courses up to uniform convergence. There are over 200 exercises ranging from simple applications to results which extend the theory describe in the text. Chapter 1 discusses Preliminaries – thereafter, the topics covered are Basic Terminology, Continuous Functions, Completedness, Compactness and Connectedness with a final chapter on Further Topics such as extension theorems, Baire's category theorem, approximation to continuous functions and separability.