
Set Theory and Metric Spaces
Irving Kaplansky(Author)
American Mathematical Society (Publisher)
Published on 30. December 1972
Book
Paperback/Softback
140 pages
978-1-4704-6384-7 (ISBN)
Description
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.
Reviews / Votes
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
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
ISBN-13
978-1-4704-6384-7 (9781470463847)
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Schweitzer Classification
Content
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
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