Stone duality for Dedekind \(\sigma\)-complete \(\ell\)-groups with order-unit
type: Item
instance of: scholarly article
title: Stone duality for Dedekind \(\sigma\)-complete \(\ell\)-groups with order-unit
zbMATH Open document ID: 1108.06011
published in: Journal of Algebra
publication date: 2006-12-07T00:00:00Z
review text: If \(G\) is a lattice-ordered group (\(\ell \)-group) then \(G\) is Dedekind \(\sigma \)-complete if every non-empty countable subset of \(G\) which is bounded above in \(G\) has a supremum in \(G\). Denote by \(\mathcal{DED}\) the category whose objects are Dedekind \(\sigma \)-complete \(\ell \)-groups with a distinguished order-unit and whose morphisms are the unit preserving \(\ell \)-group homomorphisms which, moreover, preserve all denumerable infima and suprema. The authors establish a categorical duality between \(\mathcal{DED}\) and a category \(\mathcal{W}\) consisting of basically disconnected compact Hausdorff spaces equiped with a system of closed sets. Furthemore, the restiction of this duality gives analogous topological representations for certain subclasses of \(\mathcal{DED}\).
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 06D50
zbMATH DE Number: 5078152
zbMATH Keywords: lattice-ordered abelian group
zbMATH Keywords: Stone duality
zbMATH Keywords: basically disconnected space
zbMATH Keywords: complete MV-algebra
author: Roberto Cignoli
author: Daniele Mundici
reviewed by: Jiří Rachůnek
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.05.029
OpenAlex ID: W2091380762
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DOI: 10.1016/J.JALGEBRA.2006.05.029
description: scientific article; zbMATH DE number 5078152