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Ams Chelsea Publishing Ser.: Set Theory by Felix Hausdorff (2005, Hardcover)

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About this product

Product Identifiers

PublisherAmerican Mathematical Society
ISBN-100821838350
ISBN-139780821838358
eBay Product ID (ePID)45956724

Product Key Features

Number of Pages352 Pages
Publication NameSet Theory
LanguageEnglish
SubjectSet Theory
Publication Year2005
TypeTextbook
Subject AreaMathematics
AuthorFelix Hausdorff
SeriesAms Chelsea Publishing Ser.
FormatHardcover

Dimensions

Item Height0.6 in
Item Weight23.5 Oz
Item Length9.8 in
Item Width5.9 in

Additional Product Features

Edition Number2
Intended AudienceScholarly & Professional
LCCN2005-041073
Dewey Edition22
Series Volume Number119
Dewey Decimal512.817
Table Of ContentSets 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.
SynopsisIn the early twentieth century, Hausdorff developed an axiomatic approach to topology, which continues to be the foundation of modern topology. The present book, the English translation of the third edition of Hausdorff's Mengenlehre, is a thorough introduction to his theory of point-set topology. The treatment begins with topics in the foundations of mathematics, including the basics of abstract set theory, sums and products of sets, cardinal and ordinal numbers, and Hausdorff's well-ordering theorem. The exposition then specializes to point sets, where major topics such as Borel systems, first and second category, and connectedness are considered in detail. Next, mappings between spaces are introduced. This leads naturally to a discussion of topological spaces and continuous mappings between them. Finally, the theory is applied to the study of real functions and their properties. The book does not presuppose any mathematical knowledge beyond calculus, but it does require a certain maturity in abstract reasoning; qualified college seniors and first-year graduate students should have no difficulty in making the material their own., Presents 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., This work is a translation into English of the Third Edition of the classic German language work Mengenlehre by Felix Hausdorff published in 1937. From the Preface (1937): ''The present book has as its purpose an exposition of the most important theorems of the theory of sets, along with complete proofs, so that the reader should not find it necessary to go outside this book for supplementary details while, on the other hand, the book should enable him to undertake a more detailed study of the voluminous literature on the subject. The book does not presuppose any mathematical knowledge beyond the differential and integral calculus, but it does require a certain maturity in abstract reasoning; qualified college seniors and first year graduate students should have no difficulty in making the material their own ... The mathematician will ... find in this book some things that will be new to him, at least as regards formal presentation and, in particular, as regards the strengthening of theorems, the simplification of proofs, and the removal of unnecessary hypotheses.''
LC Classification NumberQA248.H353 2005
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