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Set Theory and Metric Spaces

Set Theory and Metric Spaces - (2nd edition

ISBN13: 978-0821826942

Cover of Set Theory and Metric Spaces (2ND)77 (ISBN 978-0821826942)
ISBN13: 978-0821826942
ISBN10: 0821826948
Cover type: Hardback
Edition/Copyright: (2ND)77
Publisher: Chelsea Publishing Co.
Published: 1977
International: No

List price: $34.00

Set Theory and Metric Spaces - (2ND)77 edition

ISBN13: 978-0821826942

Irving Kaplansky

ISBN13: 978-0821826942
ISBN10: 0821826948
Cover type: Hardback
Edition/Copyright: (2ND)77
Publisher: Chelsea Publishing Co.

Published: 1977
International: No
Summary

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.

Table of Contents

Basic Set Theory

1.1 Inclusion
1.2 Operations on sets
1.3 Partially ordered sets and lattices
1.4 Functions
1.5 Relations
Cartesian products

Cardinal Numbers

2.1 Countable sets
2.2 Cardinal numbers
2.3 Comparison of cardinal numbers

Zorn's lemma

2.4 Cardinal addition
2.5 Cardinal multiplication
2.6 Cardinal exponentiation
Well-Ordering

The Axiom of Choice

3.1 Well-ordered sets
3.2 Ordinal numbers
3.3 The axiom of choice
3.4 The continuum problem

Basic Properties of Metric Spaces

4.1 Definitions and examples
4.2 Open sets
4.3 Convergence
Closed sets
4.4 Continuity

Completeness, Separability, and Compactness

5.1 Completeness
5.2 Separability
5.3 Compactness

Additional Topics

6.1 Product spaces
6.2 A fixed-point theorem
6.3 Category

Appendixes

1 Examples of metric spaces
2 Set theory and algebra
3 The transition to topological spaces
Selected bibliography
Index