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Preface

1 Prelude to Modern Analysis
1£®1 Introduction
1£®2 Sets and numbers
1£®3 Functions or mappings
1£®4 Countability
1£®5 Point sets
1£®6 Open and closed sets
1£®7 Sequences
1£®8 Series
1£®9 Functions of a real variable
1£®10 Uniform convergence
1£®11 Some linear algebra
1£®12 Setting off

2 Metric Spaces
2£®1 Definition of a metric space
2£®2 Examples of metric spaces
2£®3 Solved problems
2£®4 Exercises
2£®5 Convergence in a metric space
2£®6 Examples on completeness
2£®7 Subspace of a metric space
2£®8 Solved problems
2£®9 Exercises

3 The Fixed Point Theorem and its Applications
3£®1 Mappings between metric spaces
3£®2 The fixed point theorem
3£®3 Applications
3£®4 Perturbation mappings
3£®5 Exercises

4 Compactness
4£®1 Compact sets
4£®2 Ascoli's theorem
4£®3 Application to approximation theory
4£®4 Solved problems
4£®5 Exercises

5 Topological Spaces
5£®1 Definitions and examples
5£®2 Closed sets
5£®3 Compact sets
5£®4 Continuity in topological spaces
5£®5 Homeomorphisms; connectedness
5£®6 Solved problems
5£®7 Exercises
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6 Normed Vector Spaces
7 Mappings on Normed Spaces
8 Inner Product Spaces
9 Hilbert Space

Bibliography
Selected Solutions
Index
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