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Set Theory and Metric Spaces

AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Available Formats:
Softcover ISBN: 978-1-4704-6384-7
Product Code: CHEL/298.H.S
List Price: $37.00 MAA Member Price:$33.30
AMS Member Price: $33.30 Electronic ISBN: 978-1-4704-6385-4 Product Code: CHEL/298.H.E List Price:$37.00
MAA Member Price: $33.30 AMS Member Price:$33.30
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List Price: $55.50 MAA Member Price:$49.95
AMS Member Price: $49.95 Click above image for expanded view Set Theory and Metric Spaces AMS Chelsea Publishing: An Imprint of the American Mathematical Society Available Formats:  Softcover ISBN: 978-1-4704-6384-7 Product Code: CHEL/298.H.S  List Price:$37.00 MAA Member Price: $33.30 AMS Member Price:$33.30
 Electronic ISBN: 978-1-4704-6385-4 Product Code: CHEL/298.H.E
 List Price: $37.00 MAA Member Price:$33.30 AMS Member Price: $33.30 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$55.50 MAA Member Price: $49.95 AMS Member Price:$49.95
• Book Details

AMS Chelsea Publishing
Volume: 2981972; 140 pp
MSC: Primary 03; Secondary 54;

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.

• Cover
• Title 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
• Appendixes
• 1. Examples of Metric Spaces
• 2. Set Theory and Algebra
• 3. The Transition to Topological Spaces
• Selected Bibliography
• Index
• Back Cover
• Reviews

• 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.

• Kaplansky has a well-deserved reputation for his expository talents. The selection of topics is excellent.

Lance Small, UC San Diego
• Request Review Copy
• Get Permissions
Volume: 2981972; 140 pp
MSC: Primary 03; Secondary 54;

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.

• Cover
• Title 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
• Appendixes
• 1. Examples of Metric Spaces
• 2. Set Theory and Algebra
• 3. The Transition to Topological Spaces
• Selected Bibliography
• Index
• Back 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.