Softcover ISBN:  9781470463847 
Product Code:  CHEL/298.H.S 
List Price:  $37.00 
MAA Member Price:  $33.30 
AMS Member Price:  $33.30 
Electronic ISBN:  9781470463854 
Product Code:  CHEL/298.H.E 
List Price:  $37.00 
MAA Member Price:  $33.30 
AMS Member Price:  $33.30 

Book DetailsAMS Chelsea PublishingVolume: 298; 1972; 140 ppMSC: 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.
ReadershipUndergraduates and graduate students interested in set theory and metric spaces.

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


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 wellordering, 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 welldeserved reputation for his expository talents. The selection of topics is excellent.
Lance Small, UC San Diego


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

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

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 wellordering, 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 welldeserved reputation for his expository talents. The selection of topics is excellent.
Lance Small, UC San Diego