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Summary: This book is based on notes from a course on set theory and metric spaces taught by Edwin Spanier, and also incorporates with his permission numerous exercises from those notes. The volume includes an Appendix that helps bridge the gap between metric and topological spaces, a Selected Bibliography, and an Index.Edition/Copyright: (2ND)77
Basic Set Theory
1.2 Operations on sets
1.3 Partially ordered sets and lattices
2.1 Countable sets
2.2 Cardinal numbers
2.3 Comparison of cardinal numbers
2.4 Cardinal addition
2.5 Cardinal multiplication
2.6 Cardinal exponentiation
The Axiom of Choice
3.1 Well-ordered sets
3.2 Ordinal numbers
3.3 The axiom of choice
3.4 The continuum problem
Basic Properties of Metric Spaces
4.1 Definitions and examples
4.2 Open sets
Completeness, Separability, and Compactness
6.1 Product spaces
6.2 A fixed-point theorem
1 Examples of metric spaces
2 Set theory and algebra
3 The transition to topological spaces
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