Complete Boolean Algebras

We address in this chapter the theory of complete boolean algebras: We show that any complete boolean algebra (cba in the sequel) can be represented as the family of regular open sets of a compact topological space (Theorem 4.1.2 and Proposition 4.1.5), and we prove that every partial order can be completed to a cba, which is unique up to isomorphism (Theorem 4.2.4).