Introduction to the Analysis of Metric Spaces

Preface Part I. Metric Spaces and Normed Linear Spaces: 1. Definitions and examples 2. Balls and boundedness Part II. Limit Processes: 3. Convergence and completeness 4. Cluster points and closure 5. Application: Banach's fixed point theorem Part III. Continuity: 6. Continuity in metric spaces 7. Continuous linear mappings Part IV. Compactness: 8. Sequential compactness in metric spaces 9. Continuous functions on compact metric spaces Part V. The Metric Topology: 10. The topological analysis of metric spaces Appendices Index of notation Index.