Description
Book SynopsisThis 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.
Trade ReviewThis 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
Table of Contents
- Cover
- Title Page
- Copyright Page
- Contents
- Preface
- 1. Basic Set Theory
- 2. Cardinal Numbers
- 3. Well Ordering; The Axiom of Choice
- 4. Basic Properties of Metric Spaces
- 5. Completeness, Separability, and Compactness
- 6. Additional Topics
- Appendixes
- 1. Examples of Metric Spaces
- 2. Set Theory and Algebra
- 3. The Transition to Topological Spaces
- Selected Bibliography
- Index
- Back Cover
