On the continuity points of left-continuous t-norms
type: Item
instance of: scholarly article
title: On the continuity points of left-continuous t-norms
zbMATH Open document ID: 1047.03016
author: Sándor Jenei
author: Franco Montagna
published in: Archive for Mathematical Logic
publication date: 2004-03-07T00:00:00Z
review text: The authors show that each left-continuous t-norm can be obtained as the completion of a continuous function on some dense subset of \([0,1]^2\). As a by-product, they prove that the set of discontinuity points of a left-continuous t-norm is a first-category set of measure zero. Further, they show that not all left-continuous t-norms are isomorphic to the completion of some continuous t-norm on~\(Q\cap[0,1]\) (the set of all rational numbers from the unit interval). However, they prove that at least all weakly cancellative ones possess this property. Finally, they characterize those continuous t-norms on \(Q\cap[0,1]\) whose completion is continuous.
reviewed by: Rostislav Horčík
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 06F05
zbMATH DE Number: 2051464
zbMATH Keywords: t-norm
zbMATH Keywords: continuity
zbMATH Keywords: left-continuity
zbMATH Keywords: residuated lattice
MaRDI profile type: Publication
full work available at URL: s00153-003-0182-2
OpenAlex ID: W1992148376
DOI: 10.1007/S00153-003-0182-2
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description: scientific article; zbMATH DE number 2051464