Crawley's completion of a conditionally upper continuous lattice

Abstract

Crawley’s completion (the lattice of all complete ideals) of a conditionally upper continuous lattice L is an upper regular homomorphic image of the lattice of ideals of L. After examining the consequences of this result, Crawley’s completion is characterized both as a completion of L and as the minimal upper continuous extension of L with respect to upper regular homomorphisms. © 1974 Pacific Journal of Mathematics.