Set Theory

An indispensible book for all those interested in the theory of sets and the allied branches of real variable theory."" — Bulletin of the AMS

• Sets and the Combining of Sets: 1.1 Sets1.2 Functions1.3 Sum and intersection1.4 Product and powerCardinal Numbers: 2.5 Comparison of sets2.6 Sum, product, and power2.7 The scale of cardinal numbers2.8 The elementary cardinal numbersOrder Types: 3.9 Order3.10 Sum and product3.11 The types $\aleph_0$ and $\aleph$Ordinal Numbers: 4.12 The well-ordering theorem4.13 The comparability of ordinal numbers4.14 The combining of ordinal numbers4.15 The alefs4.16 The general concept of productSystems of Sets: 5.17 Rings and fields5.18 Borel systems5.19 Suslin setsPoint Sets: 6.20 Distance6.21 Convergence6.22 Interior points and border points6.23 The $\alpha, \beta$, and $\gamma$ points6.24 Relative and absolute concepts6.25 Separable spaces6.26 Complete spaces6.27 Sets of the first and second categories6.28 Spaces of sets6.29 ConnectednessPoint Sets and Ordinal Numbers: 7.30 Hulls and kernels7.31 Further applications of ordinal numbers7.32 Borel and Suslin sets7.33 Existence proofs7.34 Criteria for Borel setsMappings of Two Spaces: 8.35 Continuous mappings8.36 Interval-images8.37 Images of Suslin sets8.38 Homeomorphism8.39 Simple curves8.40 Topological spacesReal Functions: 9.41 Functions and inverse image sets9.42 Functions of the first class9.43 Baire functions9.44 Sets of convergenceSupplement: 10.45 The Baire condition10.46 Half-schlicht mappingsAppendixesBibliographyFurther referencesIndex