Book:Felix Hausdorff/Set Theory/Fourth Edition

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Felix Hausdorff: Set Theory (4th Edition)

Published $1991$, Chelsea Publishing Company

ISBN 0-8284-1119-0 (translated by John R. Aumann).


Subject Matter

Translation into English of 1937: Felix Hausdorff: Mengenlehre (3rd ed.)

Fourth edition of 1957: Felix Hausdorff: Set Theory (translated by John R. Aumann)


Contents

Editor's Preface
Preface to the Second English Edition
From the Preface to the Second Edition
Preface to Third Edition
Preliminary Remarks
I. Sets and the Combining of Sets
$\S 1$. Sets
$\S 2$. Functions
$\S 3$. Sum and Intersection
$\S 4$. Product and Power
II. Cardinal Numbers
$\S 5$. Comparison of Sets
$\S 6$. Sum, Product and Power
$\S 7$. The Scale of Cardinal Numbers
$\S 8$. The Elementary Cardinal Numbers
III. Order Types
$\S 9$. Order
$\S 10$. Sum, Product and Power
$\S 11$. The Types $\aleph_0$ and $\aleph$
IV. Ordinal Numbers
$\S 12$. The Well-Ordering Theorem
$\S 13$. The Comparability of Ordinal Numbers
$\S 14$. The Combining of Ordinal Numbers
$\S 15$. The Alefs
$\S 16$. The General Concept of Product
V. Systems of Sets
$\S 17$. Rings and Fields
$\S 18$. Borel Systems
$\S 19$. Suslin Sets
VI. Point Sets
$\S 20$. Distance
$\S 21$. Convergence
$\S 22$. Interior Points and Border Points
$\S 23$. The $\alpha$, $\beta$ and $\gamma$ Points
$\S 24$. Relative and Absolute Concepts
$\S 25$. Separable Spaces
$\S 26$. Complete Spaces
$\S 27$. Sets of the First and Second Categories
$\S 28$. Spaces of Sets
$\S 29$. Connectedness
VII. Point Sets and Ordinal Numbers
$\S 30$. Hulls and Kernels
$\S 31$. Further Applications of Ordinal Numbers
$\S 32$. Borel and Suslin Sets
$\S 33$. Existence Proofs
$\S 34$. Criteria for Borel Sets
VIII. Mappings of Two Spaces
$\S 35$. Continuous Mappings
$\S 36$. Interval-Images
$\S 37$. Images of Suslin Sets
$\S 38$. Homeomorphism
$\S 39$. Simple Curves
$\S 40$. Topological Spaces
IX. Real Functions
$\S 41$. Functions and Inverse Image Sets
$\S 42$. Functions of the First Class
$\S 43$. Baire Functions
$\S 44$. Sets of Convergence
X. Supplement
$\S 45$. The Baire Condition
$\S 46$. Half-sclicht Mappings
Appendixes
Bibliography
Further References
Index