Inverse limits in the category of locales
type: Item
instance of: scholarly article
title: Inverse limits in the category of locales
zbMATH Open document ID: 0904.18003
DOI: 10.1007/BF02879935
author: Wei He
author: Yingming Liu
published in: Science in China. Series A
publication date: 1998-12-29T00:00:00Z
review text: The authors give an explicit construction of filtered colimits in the category of frames -- equivalently, of (cofiltered) inverse limits in the category of locales. Using their construction, they give direct proofs that the limit of an inverse system of locales whose bonding maps are epimorphisms projects epimorphically onto each term of the system (this result was first conjectured by \textit{M. Barr}, and proved by \textit{A. Joyal} and \textit{M. Tierney} by exploiting the relations between frames and sup-lattices); and that an arbitrary inverse limit of compact locales is compact (which was proved, under the additional hypothesis that the bonding maps are epimorphic, by the reviewer and \textit{S. J. Vickers} exploiting the relations between frames and preframes). A number of topological applications are given, and their relationship to the Boolean prime ideal theorem is discussed.
Mathematics Subject Classification ID: 18A30
Mathematics Subject Classification ID: 06B23
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 54B30
zbMATH DE Number: 1187434
zbMATH Keywords: filtered colimits
zbMATH Keywords: frames
zbMATH Keywords: inverse limits
zbMATH Keywords: locales
zbMATH Keywords: sup-lattices
zbMATH Keywords: preframes
zbMATH Keywords: Boolean prime ideal theorem
reviewed by: Peter Johnstone
MaRDI profile type: Publication
cites work: Atomless Parts of Spaces.
cites work: Q3978977
cites work: Q3965241
cites work: Direct limits of meet-continuous lattices
cites work: Almost maximal ideals
cites work: Prime ideals yield almost maximal ideals
full work available at URL: https://doi.org/10.1007/bf02879935
OpenAlex ID: W1979065873
description: scientific article; zbMATH DE number 1187434