Book:Paul Halmos/Introduction to Boolean Algebras

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Paul Halmos and Steven Givant: Introduction to Boolean Algebras

Published $2008$, Springer

ISBN 978-0387402932.


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

It is an extensive rewriting of Halmos's 1963 Lectures on Boolean Algebras.


Subject Matter


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