Some typical classes of t-norms and the 1-Lipschitz Condition

This paper studies the relation between the satisfaction of the Lipschitz condition by t-norms for constant 1 (1- Lipschitz condition) and some other properties of t-norms. In this sense, we will consider some well know classes of continuous t-norms, such as Archimedean and non Archimedean, and the nilpotent and strict subclasses of Archimedean t-norms. Also will be proved that the unique automorphism which preserves the 1- Lipschitz condition of any t-norm is the identity.