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Set Theory
 
Felix Hausdorff
Set Theory
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-6494-3
Product Code:  CHEL/119.S
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
eBook ISBN:  978-1-4704-6497-4
Product Code:  CHEL/119.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Softcover ISBN:  978-1-4704-6494-3
eBook: ISBN:  978-1-4704-6497-4
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
Add to cart
Set Theory
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Set Theory
Felix Hausdorff
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-6494-3
Product Code:  CHEL/119.S
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
eBook ISBN:  978-1-4704-6497-4
Product Code:  CHEL/119.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Softcover ISBN:  978-1-4704-6494-3
eBook ISBN:  978-1-4704-6497-4
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
Add to cart
  • Book Details
     
     
    AMS Chelsea Publishing
    Volume: 119; 1957; 352 pp
    MSC: 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.”
    Readership

    Graduate 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 Well-Ordering 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. Interval-Images
    • § 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. Half-schlicht 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
AMS Chelsea Publishing
Volume: 119; 1957; 352 pp
MSC: 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.”
Readership

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 Well-Ordering 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. Interval-Images
  • § 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. Half-schlicht 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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