Characterization of some topological semigroups whose level curves are homothetic (Q1061321)

Generalizing a previous result by the author and \textit{A. Sklar} (to appear in Aequationes Math.) the following is proved: Let \(T: [0,1]\times [0,1]\to [0,1]\) be a non-strict Archimedean t-norm. The level curves \(\{(x,y)| \quad T(x,y)=a\},\) \(0\leq a<1\) are homothetic, if and only if \(T(x,y)=\max (1-[(1-x)^{1/c}+(1-y)^{1/c}]^ c,0),\) where c is a positive real number.