Book:Paul Halmos/Introduction to Boolean Algebras

This book is part of Springer's Undergraduate Texts in Mathematics series.

It is an extensive rewriting of Halmos's 1963.

Subject Matter

 * Boolean Algebras

Contents

 * Preface
 * 1 Boolean Rings
 * 2 Boolean Algebras
 * 3 Boolean Algebras Versus Rings
 * 4 The Principle of Duality
 * 5 Fields of Sets
 * 6 Elementary Relations
 * 7 Order
 * 8 Infinite Operations
 * 9 Topology
 * 10 Regular Open Sets
 * 11 Subalgebras
 * 12 Homomorphisms
 * 13 Extensions of Homomorphisms
 * 14 Atoms
 * 15 Finite Boolean Algebras
 * 16 Atomless Boolean Algebras
 * 17 Congruences and Quotients
 * 18 Ideals and Filters
 * 19 Lattices of Ideals
 * 20 Maximal Ideals
 * 21 Homomorphism and Isomorphism Theorems
 * 22 The Representation Theorem
 * 23 Canonical Extensions
 * 24 Complete Homomorphisms and Complete Ideals
 * 25 Completions
 * 26 Products of Algebras
 * 27 Isomorphisms of Factors
 * 28 Free Algebras
 * 29 Boolean $\sigma$-algebras
 * 30 The Countable Chain Condition
 * 31 Measure Algebras
 * 32 Boolean Spaces
 * 33 Continuous Functions
 * 34 Boolean Algebras and Boolean Spaces
 * 35 Duality for Ideals
 * 36 Duality for Homomorphisms
 * 37 Duality for Subalgebras
 * 38 Duality for Completeness
 * 39 Boolean $\sigma$-spaces
 * 40 The Representation of $\sigma$-algebras
 * 41 Boolean Measure Spaces
 * 42 Incomplete Algebras
 * 43 Duality for Products
 * 44 Sums of Algebras
 * 45 Isomorphisms of Countable Factors
 * Epilogue
 * A Set Theory
 * B Hints to Selected Exercises
 * References
 * Index