*(English)*Zbl 0896.04001

Reprint of the third edition (1978; Zbl 0488.04001). See also the review of the third German edition (1935; Zbl 0012.20302).

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. Appendices. Bibliography. Further references. Index.

##### MSC:

03-01 | Textbooks (mathematical logic) |

03Exx | Set theory |

01A75 | Collected or selected works |

54-01 | Textbooks (general topology) |

54H05 | Descriptive set theory (topological aspects) |

26A21 | Classification of functions of one real variable; Baire classification |