Book:Paul R. Halmos/Lectures on Boolean Algebras

Paul R. Halmos: Lectures on Boolean Algebras

Published $\text {1963}$, D. Van Nostrand Company, Inc.

Subject Matter

• Boolean Algebras

Contents

1 Boolean rings

2 Boolean algebras

3 Fields of sets

4 Regular open sets

5 Elementary relations

6 Order

7 Infinite operations

8 Subalgebras

9 Homomorphisms

10 Free algebras

11 Ideals and filters

12 The homomorphism theorem

13 Boolean $\sigma$-algebras

14 The countable chain condition

15 Measure algebras

16 Atoms

17 Boolean spaces

18 The representation theorem

19 Duality for ideals

20 Duality for homomorphisms

21 Completion

22 Boolean $\sigma$-spaces

23 The representation of $\sigma$-algebras

24 Boolean measure spaces

25 Incomplete algebras

26 Products of algebras

27 Sums of algebras

28 Isomorphisms of factors

29 Isomorphisms of countable factors

30 Retracts

31 Projective algebras

32 Injective algebras

Epilogue

Index