Topological representation of lattice homomorphisms
type: Item
instance of: scholarly article
title: Topological representation of lattice homomorphisms
zbMATH Open document ID: 1332.54193
author: Wojciech Bielas
author: Aleksander Błaszczyk
published in: Topology and its Applications
publication date: 2015-12-18T00:00:00Z
review text: The authors state that if \(\mathbf{NLat}\) denotes the category of normal and distributive lattices with \(\mathbf{0}\) and \(\mathbf{1}\) and homomorphisms, and \(\mathbf{Comp}\) denotes the category of compact Hausdorff spaces and continuous mappings, then there exists a contravariant functor \(Ult:\mathbf{NLat} \rightarrow \mathbf{Comp}\), which when restricted to the subcategory of Boolean lattices coincides with the functor known from the theory of Stone Duality. Furthermore it carries monomorphisms into surjections, but need not carry epimorphisms into injections. They then illustrate how the result can be used to obtain several classical topological theorems.
Mathematics Subject Classification ID: 54H10
Mathematics Subject Classification ID: 06D05
zbMATH DE Number: 6521998
zbMATH Keywords: distributive lattice
zbMATH Keywords: Wallman functor
zbMATH Keywords: Stone duality
zbMATH Keywords: Boolean algebras
reviewed by: Hans Peter Künzi
MaRDI profile type: Publication
full work available at URL: j.topol.2015.05.010
OpenAlex ID: W647307092
cites work: Q4449470
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DOI: 10.1016/J.TOPOL.2015.05.010
description: scientific article; zbMATH DE number 6521998