Description
Book SynopsisPresents various theorems of the theory of sets along with complete proofs. This book discusses strengthening of theorems, the simplification of proofs, and the removal of unnecessary hypotheses.
Trade ReviewAn indispensible book for all those interested in the theory of sets and the allied branches of real variable theory."" —
Bulletin of the AMSTable of Contents
- Sets and the Combining of Sets: 1.1 Sets
- 1.2 Functions
- 1.3 Sum and intersection
- 1.4 Product and power
- Cardinal Numbers: 2.5 Comparison of sets
- 2.6 Sum, product, and power
- 2.7 The scale of cardinal numbers
- 2.8 The elementary cardinal numbers
- Order Types: 3.9 Order
- 3.10 Sum and product
- 3.11 The types $\aleph_0$ and $\aleph$
- Ordinal Numbers: 4.12 The well-ordering theorem
- 4.13 The comparability of ordinal numbers
- 4.14 The combining of ordinal numbers
- 4.15 The alefs
- 4.16 The general concept of product
- Systems of Sets: 5.17 Rings and fields
- 5.18 Borel systems
- 5.19 Suslin sets
- Point Sets: 6.20 Distance
- 6.21 Convergence
- 6.22 Interior points and border points
- 6.23 The $\alpha, \beta$, and $\gamma$ points
- 6.24 Relative and absolute concepts
- 6.25 Separable spaces
- 6.26 Complete spaces
- 6.27 Sets of the first and second categories
- 6.28 Spaces of sets
- 6.29 Connectedness
- Point Sets and Ordinal Numbers: 7.30 Hulls and kernels
- 7.31 Further applications of ordinal numbers
- 7.32 Borel and Suslin sets
- 7.33 Existence proofs
- 7.34 Criteria for Borel sets
- Mappings of Two Spaces: 8.35 Continuous mappings
- 8.36 Interval-images
- 8.37 Images of Suslin sets
- 8.38 Homeomorphism
- 8.39 Simple curves
- 8.40 Topological spaces
- Real Functions: 9.41 Functions and inverse image sets
- 9.42 Functions of the first class
- 9.43 Baire functions
- 9.44 Sets of convergence
- Supplement: 10.45 The Baire condition
- 10.46 Half-schlicht mappings
- Appendixes
- Bibliography
- Further references
- Index
