Superatomic Boolean algebras
George Day · Pacific Journal of Mathematics · 1967
A Boolean algebra B can be imbedded in a complete Boolean algebra C in such a way that all homomorphisms of B into complete Boolean algebras can be extended to complete homomorphisms on C if and only if B is superatomic, that is, every homomorphic image of B is atomic.This paper is a study of the structure of superatomic Boolean algebras, through the development of techniques of construction and classification, and through the representation of these algebras as compact Hausdorff clairsemέ spaces.