On the congruence lattice of a frame

Bernhard Banaschewski, J. L. Frith and C. R. A. Gilmour

Vol. 130 (1987), No. 2, 209–213

DOI: 10.2140/pjm.1987.130.209

Abstract

Recall that the Skula modification SkX of a topological space X is the space with the same underlying set as X whose topology is generated by the topology ΩX of X and the closed subsets of X. R. E. Hoffmann characterizes the spaces X for which SkX is compact Hausdorff as the noetherian sober spaces. The object of this note is to give a simple proof of the analogue of this characterization for frames and to show how our result for frames applies to the original one for spaces.

Mathematical Subject Classification 2000

Primary: 06C99

Secondary: 54A99

Milestones

Received: 25 September 1986

Revised: 13 January 1987

Published: 1 December 1987