Set Theory and Metric Spaces (Ams Chelsea Publishing)

Set Theory and Metric Spaces (Ams Chelsea Publishing)

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  • 製本 Hardcover:ハードカバー版／ページ数 140 p.
  • 言語 ENG
  • 商品コード 9780821826942

Full Description

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.

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.