On the congruence lattice of a frame
type: Item
instance of: scholarly article
title: On the congruence lattice of a frame
zbMATH Open document ID: 0637.06006
author: John Frith
author: Bernhard Banaschewski
author: Christopher Gilmour
published in: Pacific Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 06D20
Mathematics Subject Classification ID: 54B30
zbMATH DE Number: 4037895
zbMATH Keywords: congruence lattice
zbMATH Keywords: frame
zbMATH Keywords: lattice of nuclei
zbMATH Keywords: Skula modification of a topological space
reviewed by: Peter Johnstone
MaRDI profile type: Publication
full work available at URL: pjm.1987.130.209
OpenAlex ID: W2040237292
DOI: 10.2140/PJM.1987.130.209
description: scientific article; zbMATH DE number 4037895