Book:Paul Halmos/Introduction to Boolean Algebras

Paul Halmos and Steven Givant: Introduction to Boolean Algebras

Published $\text {2008}$, 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

• 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