Set Theory and Metric Spaces

Name: Set Theory and Metric Spaces
Price: 54.0 USD
Availability: InStock
ISBN: 9780821826942

ISBN-10: 0821826948

ISBN-13: 9780821826942

Edition: N/A

Authors: Irving Kaplansky

List price: $37.00

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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 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…

Book details

List price: $37.00
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



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