an:04037895
Zbl 0637.06006
Banaschewski, Bernhard; Frith, J. L.; Gilmour, C. R. A.
On the congruence lattice of a frame
EN
Pac. J. Math. 130, No. 2, 209-213 (1987).
00165753
1987
j
06D20 54B30
congruence lattice; frame; lattice of nuclei; Skula modification of a topological space
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.
P.T.Johnstone