Set Theory and Metric Spaces

This is a book that could profitably be read by many graduate students or by seniors in strong major programs … has a number of good features. There are many informal comments scattered between the formal development of theorems and these are done in a light and pleasant style. … There is a complete proof of the equivalence of the axiom of choice, Zorn's Lemma, and well-ordering, as well as a discussion of the use of these concepts. There is also an interesting discussion of the continuum problem … The presentation of metric spaces before topological spaces … should be welcomed by most students, since metric spaces are much closer to the ideas of Euclidean spaces with which they are already familiar.- Canadian Mathematical Bulletin;""Kaplansky has a well-deserved reputation for his expository talents. The selection of topics is excellent.""- Lance Small, UC San Diego

• CoverTitle PageCopyright PageContentsPreface1. Basic Set Theory2. Cardinal Numbers3. Well Ordering; The Axiom of Choice4. Basic Properties of Metric Spaces5. Completeness, Separability, and Compactness6. Additional TopicsAppendixes1. Examples of Metric Spaces2. Set Theory and Algebra3. The Transition to Topological SpacesSelected BibliographyIndexBack Cover