Theory of SetsThis is a softcover reprint of the English translation of 1968 of N. Bourbaki's, Thorie des Ensembles (1970). |
Contents
| 11 | |
Definition of quantifiers | 37 |
Typical quantifiers | 43 |
Appendix Characterization of terms and relations | 50 |
Exercises for 1 | 59 |
THEORY OF SETS | 65 |
Restrictions and extensions of functions | 82 |
Union and intersection of a family of sets | 90 |
Exercises for 6 | 241 |
Exercises for 1 | 251 |
Bibliography | 257 |
Morphisms and derived structures | 271 |
Universal mappings | 283 |
TOPOLOGICAL VECTOR SPACES | 288 |
Exercises for 1 | 289 |
Historical Note on Chapters IIV | 296 |
Product of a family of sets | 103 |
Equivalence relations | 111 |
Mappings compatible with equivalence relations | 118 |
ORDERED SETS CARDINALS INTEGERS | 131 |
Wellordered sets | 148 |
Natural integers Finite sets | 166 |
Infinite sets | 183 |
Inverse limits and direct limits | 191 |
Exercises for 1 | 212 |
Exercises for 2 | 221 |
Exercises for 3 | 229 |
Exercises for 5 | 235 |
24 | 304 |
72 | 308 |
INTEGRATION | 311 |
28 | 312 |
81 | 326 |
30 | 327 |
38 | 335 |
Bibliography | 343 |
| 387 | |
Axioms and schemes of the theory of sets | 414 |
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Common terms and phrases
A₁ abuse of language algebraic assembly bijection called canonical bijection canonical mapping Card cardinal Chapter COROLLARY Deduce defined definition denoted direct system E₁ equipotent equivalence class equivalence relation example Exercise exists a unique family of sets faß follows greatest element hence hypothesis identity mapping implies index set induction injection integer intersection inverse system isomorphism lattice least element least upper bound Lemma Let f let ƒ Let G logical mapping f mapping ƒ mathematics maximal element morphism non-empty notation order relation ordinal sum partition pr₁G proof Proposition prove quotient quotient set relation 3x resp satisfies segment sequence set and let set F set of subsets Show species of structures structure of species Suppose surjective system of sets term theorem theory of sets topology totally ordered set union well-ordered set ΕΙ λει