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 BulletinKaplansky has a well-deserved reputation for his expository talents. The selection of topics is excellent.— Lance Small, UC San DiegoThis 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.
- 154 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Set Theory and Metric Spaces
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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
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Yes, you can access Set Theory and Metric Spaces by Irving Kaplansky in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.