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Set Theory and Metric Spaces

Irving Kaplansky
Publisher: 
American Mathematical Society
Publication Date: 
2001
Number of Pages: 
140
Format: 
Hardcover
Edition: 
2
Series: 
AMS Chelsea Publishing
Price: 
30.00
ISBN: 
978-0821826942
Category: 
Textbook
BLL Rating: 

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

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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

Dummy View - NOT TO BE DELETED