Set theory and metric spaces
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.
Print Book, English, cop. 1977
AMS Chelsey Publishing, Providence, Rhode Island, cop. 1977
XII, 140 p. : il. ; 23 cm.
9780821826942, 0821826948
1123947976
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.