Halmos P. Lectures on Boolean Algebras 2018

Textbook in PDF format

Starting with Boolean rings and algebras, the treatment examines fields of sets, regular open sets, elementary relations, infinite operations, subalgebras, homomorphisms, free algebras, ideals and filters, and the homomorphism theorem. Additional topics include measure algebras, Boolean spaces, the representation theorem, duality for ideals and for homomorphisms, Boolean measure spaces, isomorphisms of factors, projective and injective algebras, and many other subjects. Several chapters conclude with stimulating exercises; the solutions are not included.
Boolean rings
Boolean algebras
Fields of sets
Regular open sets
Elementary relations
Order
Infinite operations
Subalgebras
Homomorphisms
1Free algebras
Ideals and filters
The homomorphism theorem
Boolean Пѓ-algebras
The countable chain condition
Measure algebras
Atoms
Boolean spaces
The representation theorem
Duality for ideals
Duality for homomorphisms
Completion
Boolean Пѓ-spaces
The representation of Пѓ-algebras
Boolean measure spaces
Incomplete algebras
Products of algebras
Sums of algebras
Isomorphisms of factors
Isomorphisms of countable factors
Retracts
Projective algebras
Injective algebras