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Edition: 2ND 77

Copyright: 1977

Publisher: Chelsea Publishing Co.

Published: 1977

International: No

Copyright: 1977

Publisher: Chelsea Publishing Co.

Published: 1977

International: No

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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.

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

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

Publisher Info

Publisher: Chelsea Publishing Co.

Published: 1977

International: No

Published: 1977

International: No

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