On the congruence lattice of a frame
It is well known that the congruence lattice of a frame L (or its isomorph, the lattice of nuclei of L) is itself a frame. The main reslt of this paper is that the congruence lattice of L is compact precisely when L is Noetherian; this is then applied (via a reslt of H. Simmons characterizing the space of points of the congruence lattice of L) to recover a result of R.-E. Hoffmann on when the Skula modification of a topological space is compact.
Skula modification of a topological space
scientific article; zbMATH DE number 4037895