Introduction to Boolean Algebras

Front Matter....Pages 1-14
Boolean Rings....Pages 1-7
Boolean Algebras....Pages 8-13
Boolean Algebras Versus Rings....Pages 14-19
The Principle of Duality....Pages 20-23
Fields of Sets....Pages 24-30
Elementary Relations....Pages 31-37
Order....Pages 38-44
Infinite Operations....Pages 45-52
Topology....Pages 53-65
Regular Open Sets....Pages 66-73
Subalgebras....Pages 74-88
Homomorphisms....Pages 89-104
Extensions of Homomorphisms....Pages 105-116
Atoms....Pages 117-126
Finite Boolean Algebras....Pages 127-133
Atomless Boolean Algebras....Pages 134-141
Congruences and Quotients....Pages 142-148
Ideals and Filters....Pages 149-163
Lattices of Ideals....Pages 164-170
Maximal Ideals....Pages 171-177
Homomorphism and Isomorphism Theorems....Pages 178-187
The Representation Theorem....Pages 188-192
Canonical Extensions....Pages 193-199
Complete Homomorphisms and Complete Ideals....Pages 200-213
Completions....Pages 214-220
Products of Algebras....Pages 221-242
Isomorphisms of Factors....Pages 243-255
Free Algebras....Pages 256-267
Boolean s-algebras....Pages 268-281
The Countable Chain Condition....Pages 282-287
Measure Algebras....Pages 288-299
Boolean Spaces....Pages 300-311
Continuous Functions....Pages 312-325
Boolean Algebras and Boolean Spaces....Pages 326-337
Duality for Ideals....Pages 338-346
Duality for Homomorphisms....Pages 347-358
Duality for Subalgebras....Pages 359-367
Duality for Completeness....Pages 368-372
Boolean s-spaces....Pages 373-377
The Representation of s-algebras....Pages 378-383
Boolean Measure Spaces....Pages 384-389
Incomplete Algebras....Pages 390-395
Duality for Products....Pages 396-421
Sums of Algebras....Pages 422-438
Isomorphisms of Countable Factors....Pages 439-446
Back Matter....Pages 1-128