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Document Type: | Book |
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All Authors / Contributors: |
Irving Kaplansky |
ISBN: | 9780821826942 0821826948 |
OCLC Number: | 316231043 |
Notes: | "The text of the second edition differs only slightly from that of the first edition."--Literaturverz. S. 134 - 135. |
Description: | XII, 140 Seiten : Illustrationen ; 24 cm |
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. |
Responsibility: | Irving Kaplansky. |
Reviews
Publisher Synopsis
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 Read more...

