Compact spaces and distributive lattices.
type: Item
instance of: scholarly article
title: Compact spaces and distributive lattices.
zbMATH Open document ID: 1034.54005
DOI: 10.1016/S0022-4049(03)00088-4
author: Thierry Coquand
published in: Journal of Pure and Applied Algebra
publication date: 2003-09-15T00:00:00Z
review text: The author presents a general construction connecting compact locales and distributive lattices that allows to reduce results about compact locales to distributive lattices. In the paper there are two applications of the reduction: the localic version of Tychonoff's theorem on the compactness of products and the localic version of Steenrod's theorem on the compactness of inverse limits. The feature of these arguments is that they can be formulated both in topos theory and in a predicative theory.
Mathematics Subject Classification ID: 54A99
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 03E25
Mathematics Subject Classification ID: 03F65
Mathematics Subject Classification ID: 06D22
Mathematics Subject Classification ID: 54D30
zbMATH DE Number: 1981481
zbMATH Keywords: compact locales
zbMATH Keywords: distributive lattices
zbMATH Keywords: Tychonoff's theorem
zbMATH Keywords: Steenrod's theorem
reviewed by: Bohumil František Šmarda
MaRDI profile type: Publication
cites work: Q3762311
cites work: Q3819682
cites work: Q4944905
cites work: An intuitionistic proof of Tychonoff's theorem
cites work: Steenrod's theorem for locales
cites work: Tychonoff's theorem without the axiom of choice
cites work: Q3711309
cites work: Q3978977
description: scientific article; zbMATH DE number 1981481