Sobriety and spatiality in varieties of algebras
type: Item
instance of: scholarly article
title: Sobriety and spatiality in varieties of algebras
zbMATH Open document ID: 1177.54004
author: Sergejs Solovjovs
published in: Fuzzy Sets and Systems
publication date: 2009-08-28T00:00:00Z
review text: This paper extends the fundamental adjunction between the categories of topological spaces and locales (that paved the ground for the development of locale theory and point-free topology), and its analogue for fuzzy topology, to an arbitrary variety of algebras \textbf{A}. For this, the author introduces the category \(Q\)-\textbf{Top} of \(Q\)-topological spaces and \(Q\)-continuous maps, for an algebra \(Q\) of \textbf{A}. The corresponding notions of \(Q\)-sobriety and \(Q\)-spatiality are studied in detail and the obtained results are illustrated in the category of algebras over a given unital commutative quantale.
reviewed by: Jorge Picado
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 06F07
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 18B99
zbMATH DE Number: 5599476
zbMATH Keywords: variety
zbMATH Keywords: \(\Omega \)-algebra
zbMATH Keywords: localic algebra
zbMATH Keywords: \(Q\)-powerset
zbMATH Keywords: \(Q\)-topology
zbMATH Keywords: \(Q\)-space
zbMATH Keywords: \(Q\)-sober \(Q\)-space
zbMATH Keywords: stratified \(Q\)-space
zbMATH Keywords: \(Q\)-spatial localic algebra
zbMATH Keywords: \(Q\)-Sierpiński space
zbMATH Keywords: quantale
zbMATH Keywords: quantale module
zbMATH Keywords: quantale algebra
zbMATH Keywords: t-norm
MaRDI profile type: Publication
full work available at URL: j.fss.2008.02.010
OpenAlex ID: W1967370057
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Sobriety and spatiality in varieties of algebras (cites work)
cites work: Fuzzy sets

Sobriety and spatiality in varieties of algebras (DOI)
DOI: 10.1016/J.FSS.2008.02.010