Ship-Ship-Hooray! Free Shipping on $25+ Details >
Set Theory and Metric Spaces

Set Theory and Metric Spaces - 2nd edition

Set Theory and Metric Spaces - 2nd edition

ISBN13: 9780821826942

ISBN10: 0821826948

Set Theory and Metric Spaces by Irving Kaplansky - ISBN 9780821826942
Edition: 2ND 77
Copyright: 1977
Publisher: Chelsea Publishing Co.
Published: 1977
International: No
Set Theory and Metric Spaces by Irving Kaplansky - ISBN 9780821826942

ISBN13: 9780821826942

ISBN10: 0821826948

Edition: 2ND 77

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

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

Top Arrow

Top