Localic Priestley duality
type: Item
instance of: scholarly article
title: Localic Priestley duality
zbMATH Open document ID: 0872.18003
DOI: 10.1016/S0022-4049(96)00169-7
author: Chris Townsend
published in: Journal of Pure and Applied Algebra
publication date: 1997-09-11T00:00:00Z
review text: What is proved here is actually not a duality but a (covariant) equivalence: that between the localic analogues of the category of ordered Stone spaces (which were introduced by \textit{H. A. Priestley} in 1970 as the duals of distributive lattices) and of the category of coherent spaces (the non-Hausdorff generalization of Stone spaces which appeared in \textit{M. H. Stone}'s 1937 representation theorem for distributive lattices). The equivalence of these two categories (both being dual to the category of distributive lattices) has been well known for some time, even on the localic level; but this is the first entirely constructive proof of the result to appear in print.
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 06E15
Mathematics Subject Classification ID: 06D05
zbMATH DE Number: 1004388
zbMATH Keywords: ordered Stone spaces
zbMATH Keywords: category of distributive lattices
zbMATH Keywords: constructive proof
zbMATH Keywords: coherent spaces
reviewed by: Peter Johnstone
MaRDI profile type: Publication
cites work: Q3711309
cites work: Q3978977
cites work: Representation of Distributive Lattices by means of ordered Stone Spaces
cites work: On the parallel between the suplattice and preframe approaches to locale theory
description: scientific article; zbMATH DE number 1004388