Weak P-subsets of Stone spaces (Q5957280)

The author investigates the Stone space \(st(B)\) of the Boolean algebra \(B\). The main theorem of the paper describes conditions which imply that \(st(A)\) is homeomorphic to a weak \(P\)-subset of \(st(B)\), where \(A,B\) are complete Boolean algebras of size \(c\). The restriction to extremally disconnected spaces, i.e., Stone spaces of complete Boolean algebras is contained in the most part of the paper. Some applications and a small generalization are given.