Book:Felix Hausdorff/Set Theory/Fourth Edition

Subject Matter

 * Set Theory

Translation into English of

Contents











 * I. 
 * $\S 1$. Sets
 * $\S 2$. Functions
 * $\S 3$. Sum and Intersection
 * $\S 4$. Product and Power


 * II. 
 * $\S 5$. Comparison of Sets
 * $\S 6$. Sum, Product and Power
 * $\S 7$. The Scale of Cardinal Numbers
 * $\S 8$. The Elementary Cardinal Numbers


 * III. 
 * $\S 9$. Order
 * $\S 10$. Sum, Product and Power
 * $\S 11$. The Types $\aleph_0$ and $\aleph$


 * IV. 
 * $\S 12$. 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. 
 * $\S 17$. Rings and Fields
 * $\S 18$. Borel Systems
 * $\S 19$. Suslin Sets


 * VI. 
 * $\S 20$. 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. 
 * $\S 30$. 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. 
 * $\S 35$. Continuous Mappings
 * $\S 36$. Interval-Images
 * $\S 37$. Images of Suslin Sets
 * $\S 38$. Homeomorphism
 * $\S 39$. Simple Curves
 * $\S 40$. Topological Spaces


 * IX. 
 * $\S 41$. Functions and Inverse Image Sets
 * $\S 42$. Functions of the First Class
 * $\S 43$. Baire Functions
 * $\S 44$. Sets of Convergence


 * X. 
 * $\S 45$. The Baire Condition
 * $\S 46$. Half-sclicht Mappings