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Zbl 0896.04001
Hausdorff, Felix
Set theory. Transl. from the German by John R. Aumann. 4th ed. (English)
[B] New York, NY: Chelsea. 352 p. \$ 28.00 (1991). ISBN 0-8284-1119-0/hbk

Reprint of the third edition (1978; Zbl 0488.04001). See also the review of the third German edition (1935; Zbl 0012.20302). \par 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 2000:: *03-01 Textbooks (mathematical logic)
03Exx Set theory (logic)
01A75 Collected or selected works
54-01 Textbooks (general topology)
54H05 Descriptive set theory (topological aspects)
26A21 Classification of functions of one real variable

Keywords: cardinal numbers; order types; well-ordering; point sets; ordinal numbers; Suslin sets; Borel sets; continuous mappings; topological spaces; real functions

Citations: Zbl 0488.04001; Zbl 0081.04601; Zbl 0012.20302; Zbl 0060.12401

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