Set Theory and Metric Spaces

ISBN-10: 0821826948
ISBN-13: 9780821826942
Edition: N/A
Authors: Irving Kaplansky
List price: $34.00
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Description: 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  More...

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Book details

List price: $34.00
Publisher: American Mathematical Society
Publication date: 5/8/2001
Binding: Hardcover
Pages: 140
Size: 6.00" wide x 9.00" long x 0.50" tall
Weight: 0.836
Language: English

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 well-ordering, 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 well-deserved reputation for his expository talents. The selection of topics is excellent. --Lance Small, UC San Diego 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
Inclusion
Operations on sets
Partially ordered sets and lattices
Functions
Relations; Cartesian products Cardinal Numbers
Countable sets
Cardinal numbers
Comparison of cardinal numbers; Zorn's lemma
Cardinal addition
Cardinal multiplication
Cardinal exponentiation Well-Ordering; The Axiom of Choice
Well-ordered sets
Ordinal numbers
The axiom of choice
The continuum problem Basic Properties of Metric Spaces
Definitions and examples
Open sets
Convergence; Closed sets
Continuity Completeness, Separability, and Compactness
Completeness
Separability
Compactness Additional Topics
Product spaces
A fixed-point theorem
Category
Appendixes
Examples of metric spaces
Set theory and algebra
The transition to topological spaces Selected
Bibliography
Index

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