**AMS Chelsea Publishing**

Volume: 119;
1957;
352 pp;
Softcover

MSC: Primary 03;

**Print ISBN: 978-1-4704-6494-3
Product Code: CHEL/119.S**

List Price: $49.00

AMS Member Price: $44.10

MAA Member Price: $44.10

**Electronic ISBN: 978-1-4704-6497-4
Product Code: CHEL/119.E**

List Price: $49.00

AMS Member Price: $44.10

MAA Member Price: $44.10

# Set Theory

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*Felix Hausdorff*

AMS Chelsea Publishing: An Imprint of the American Mathematical Society

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.

#### Reviews & Endorsements

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

-- Bulletin of the AMS

#### Table of Contents

# Table of Contents

## Set Theory

- Front Cover Front Cover11
- EDITOR'S PREFACE 34
- PREFACE TO THE SECOND ENGLISH EDITION 34
- FROM THE PREFACE TO THE SECOND EDITION 56
- PREFACE TO THE THIRD EDITION 67
- TABLE OF CONTENTS 78
- PRELIMINARY REMARKS 910
- CHAPTER I: SETS AND TIIE COMBINING OF SETS 1112
- CHAPTER II: CARDINAL NUMBERS 2829
- CHAPTER III: ORDER TYPES 4849
- CHAPTER IV: ORDINAL NUMBERS 6566
- CHAPTER V: SYSTEMS OF SETS 9091
- CHAPTER VI: POINT SETS 109110
- § 20. Distance 109110
- § 21. Convergence 119120
- § 22. Interior Points and Border Points 127128
- § 23. The α, β, and γ Points 130131
- § 24. Relative and Absolute Concepts 139140
- § 25. Separable Spaces 143144
- § 26. Complete Spaces 149150
- § 27. Sets of the First and Second Categories 159160
- § 28. Spaces of Sets 166167
- § 29. Connectedness 172173

- CHAPTER VII: POINT SETS AND ORDINAL NUMBERS 188189
- CHAPTER VIII: MAPPINGS OF TWO SPACES 221222
- CHAPTER IX: REAL FUNCTIONS 264265
- CHAPTER X: SUPPLEMENT 312313
- APPENDIXES 336337
- REFERENCES 339340
- BIBLIOGRAPHY 340341
- FURTHER REFERENCES 342343
- INDEX 347348
- Back Cover Back Cover1354