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Viser: Set Theory and Metric Spaces
Set Theory and Metric Spaces
Irving Kaplansky
(2001)
American Mathematical Society
612,00 kr.
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Detaljer om varen
- Hardback: 140 sider
- Udgiver: American Mathematical Society (Maj 2001)
- ISBN: 9780821826942
Based on notes from a course on set theory and metric spaces, this book incorporates numerous exercises from those notes. It 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.
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.
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Tlf 77 42 43 44 - email poly@polyteknisk.dk - CVR 34072655 - Sydbank Reg: 6748 Konto 0001107927