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

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

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