Left-continuity of \(t\)-norms on the \(n\)-dimensional Euclidean cube (Q963842)

Let \(I=[0,1]\). A \(t\)-norm \(T\) on \(I\) is left-continuous if and only if \(T(\sup Z)=\sup T(Z)\) \((Z\subseteq I)\) (\(T\) is sup-preserving). The aim of the paper is to show that a \(t\)-norm \(T\) on the \(n\)-dimensional Euclidean cube \(I^n\) is left-continuous if and only if \(T\) preserves direct sups.