  From an analytical point of view, for a t-norm \(\rT\) their sup-preservation property is the left-continuity of this binary function \(\rT\), i.e. the property that each one of the unary functions \(\rT_{a}(x)=\rT(a,x)\) is left-continuous. And the continuity of such a t-norm T can be characterized through the algebraic divisibility condition