Not All sigma-Complete Boolean Algebras Are Quotients of Complete BooleanAlgebras

摘要

Every compact subspace of an extremally disconnected space is a compact F-space. Dually, every homomorphic image of a complete Boolean algebra is weakly countably complete (abbreviated WCC). The class of extremally disconnected spaces is a very important class of spaces hence the problem of determining the class of closed subspaces is very fundamental. Obviously it is equally fundamental to investigate the class of quotients of complete Boolean algebras. We will deal with Boolean algebras since the Boolean algebraic notions of completeness and sigma-completeness are undoubtedly better known than the topological notions of extremally and basically disconnected spaces. (Copyright (c) 1991 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)