A note on metrics induced by copulas

In this short note, we provide a continuous triangular norm that is not a copula and that generates a metric. Thus, the 9th open problem collected in Alsina et al. [Associative Functions: Triangular Norms and Copulas, World Scientific Publishing Company, Singapore, 2006] has a negative answer.

► The metrics induced by copulas are discussed.
► We provide a continuous t-norm that is not a copula and that generates a metric.
► The 9th open problem in a recent monograph of Alsina et al. is solved.