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Softcover ISBN:  9781470464943 
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Product Code:  CHEL/119.S.B 
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Softcover ISBN:  9781470464943 
Product Code:  CHEL/119.S 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470464974 
Product Code:  CHEL/119.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Softcover ISBN:  9781470464943 
eBook ISBN:  9781470464974 
Product Code:  CHEL/119.S.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 

Book DetailsAMS Chelsea PublishingVolume: 119; 1957; 352 ppMSC: Primary 03;
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.”
ReadershipGraduate students and research mathematicians.

Table of Contents

Front Cover

EDITOR'S PREFACE

PREFACE TO THE SECOND ENGLISH EDITION

FROM THE PREFACE TO THE SECOND EDITION

PREFACE TO THE THIRD EDITION

TABLE OF CONTENTS

PRELIMINARY REMARKS

CHAPTER I: SETS AND TIIE COMBINING OF SETS

§ I. Sets

§ 2. Functions

§ 3. Sum and Intersection

§ 4. Products and Powers

CHAPTER II: CARDINAL NUMBERS

§ 5. Comparison of Sets

§ 6. Sum, Product, and Power

§ 7. The Scale of Cardinal Numbers

§ 8. The Elementary Cardinal Numbers

CHAPTER III: ORDER TYPES

§ 9. Order

§ 10. Sum and Product

§ 11. The Types N0 and N

CHAPTER IV: ORDINAL NUMBERS

§ 12. The WellOrdering Theorem

§ 13. The Comparability of Ordinal Numbers

§ 14. The Combining of Ordinal Numbers

§ 15. The Alefs

§ 16. The General Concept of Product

CHAPTER V: SYSTEMS OF SETS

§ 17. Rings and Fields

§ 18. Borel Systems

§ 19. Suslin Sets

CHAPTER VI: POINT SETS

§ 20. Distance

§ 21. Convergence

§ 22. Interior Points and Border Points

§ 23. The α, β, and γ Points

§ 24. Relative and Absolute Concepts

§ 25. Separable Spaces

§ 26. Complete Spaces

§ 27. Sets of the First and Second Categories

§ 28. Spaces of Sets

§ 29. Connectedness

CHAPTER VII: POINT SETS AND ORDINAL NUMBERS

§ 30. Hulls and Kernels

§ 31. Further Applications of Ordinal Numbers

§ 32. Borel and Suslin Sets

§ 33. Existence Proofs

§ 34. Criteria for Borel sets

CHAPTER VIII: MAPPINGS OF TWO SPACES

§ 35. Continuous Mappings

§ 36. IntervalImages

§ 37. Images of Suslin Sets

§ 38. Homeomorphism

§ 39. Simple Curves

§ 40. Topological Spaces

CHAPTER IX: REAL FUNCTIONS

§ 41. Functions and Inverse Image Sets

§ 42. Functions of the First Class

§ 43. Daire Functions

§ 44. Sets of Convergence

CHAPTER X: SUPPLEMENT

§ 45. The Baire Condition

§ 46. Halfschlicht Mappings

APPENDIXES

(A). Appendix to p. 165

( D). Appendix to p. 304

( E). Appendix to p. 39

( F). Appendix to p. 66

( B). Appendix to p. 182

( C). Appendix to § 39, 2

REFERENCES

BIBLIOGRAPHY

FURTHER REFERENCES

INDEX

Back Cover


Additional Material

Reviews

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


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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.”
Graduate students and research mathematicians.

Front Cover

EDITOR'S PREFACE

PREFACE TO THE SECOND ENGLISH EDITION

FROM THE PREFACE TO THE SECOND EDITION

PREFACE TO THE THIRD EDITION

TABLE OF CONTENTS

PRELIMINARY REMARKS

CHAPTER I: SETS AND TIIE COMBINING OF SETS

§ I. Sets

§ 2. Functions

§ 3. Sum and Intersection

§ 4. Products and Powers

CHAPTER II: CARDINAL NUMBERS

§ 5. Comparison of Sets

§ 6. Sum, Product, and Power

§ 7. The Scale of Cardinal Numbers

§ 8. The Elementary Cardinal Numbers

CHAPTER III: ORDER TYPES

§ 9. Order

§ 10. Sum and Product

§ 11. The Types N0 and N

CHAPTER IV: ORDINAL NUMBERS

§ 12. The WellOrdering Theorem

§ 13. The Comparability of Ordinal Numbers

§ 14. The Combining of Ordinal Numbers

§ 15. The Alefs

§ 16. The General Concept of Product

CHAPTER V: SYSTEMS OF SETS

§ 17. Rings and Fields

§ 18. Borel Systems

§ 19. Suslin Sets

CHAPTER VI: POINT SETS

§ 20. Distance

§ 21. Convergence

§ 22. Interior Points and Border Points

§ 23. The α, β, and γ Points

§ 24. Relative and Absolute Concepts

§ 25. Separable Spaces

§ 26. Complete Spaces

§ 27. Sets of the First and Second Categories

§ 28. Spaces of Sets

§ 29. Connectedness

CHAPTER VII: POINT SETS AND ORDINAL NUMBERS

§ 30. Hulls and Kernels

§ 31. Further Applications of Ordinal Numbers

§ 32. Borel and Suslin Sets

§ 33. Existence Proofs

§ 34. Criteria for Borel sets

CHAPTER VIII: MAPPINGS OF TWO SPACES

§ 35. Continuous Mappings

§ 36. IntervalImages

§ 37. Images of Suslin Sets

§ 38. Homeomorphism

§ 39. Simple Curves

§ 40. Topological Spaces

CHAPTER IX: REAL FUNCTIONS

§ 41. Functions and Inverse Image Sets

§ 42. Functions of the First Class

§ 43. Daire Functions

§ 44. Sets of Convergence

CHAPTER X: SUPPLEMENT

§ 45. The Baire Condition

§ 46. Halfschlicht Mappings

APPENDIXES

(A). Appendix to p. 165

( D). Appendix to p. 304

( E). Appendix to p. 39

( F). Appendix to p. 66

( B). Appendix to p. 182

( C). Appendix to § 39, 2

REFERENCES

BIBLIOGRAPHY

FURTHER REFERENCES

INDEX

Back Cover

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