**AMS Chelsea Publishing**

Volume: 298;
1972;
140 pp;
Softcover

MSC: Primary 03;
Secondary 54

**Print ISBN: 978-1-4704-6384-7
Product Code: CHEL/298.H.S**

List Price: $37.00

AMS Member Price: $33.30

MAA Member Price: $33.30

**Electronic ISBN: 978-1-4704-6385-4
Product Code: CHEL/298.H.E**

List Price: $37.00

AMS Member Price: $33.30

MAA Member Price: $33.30

# Set Theory and Metric Spaces

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*Irving Kaplansky*

AMS Chelsea Publishing: An Imprint of the American Mathematical Society

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.

#### Readership

Undergraduates and graduate students interested in set theory and metric spaces.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Set Theory and Metric Spaces

- Cover 11
- Title Page 44
- Copyright Page 55
- Contents 88
- Preface 1212
- 1. Basic Set Theory 1414
- 2. Cardinal Numbers 3434
- 3. Well Ordering; The Axiom of Choice 6262
- 4. Basic Properties of Metric Spaces 8080
- 5. Completeness, Separability, and Compactness 9797
- 6. Additional Topics 119119
- Appendixes 128128
- 1. Examples of Metric Spaces 130130
- 2. Set Theory and Algebra 135135
- 3. The Transition to Topological Spaces 140140
- Selected Bibliography 146146
- Index 150150
- Back Cover 154154