On continuous triangular norms

The problem of converging to any given continuous triangular-norm by a. sequence of continuous Archimedean triangular-norms is studied. Such a sequence is built up in a constructive way. The class of well-founded triangular-norms is introduced. It is proved that a sequence of triangular-norms converges to a given continuous triangular-norm if and only if this convergence is uniform. Finally, we prove that every continuous triangular norm is a uniform limit of continuous Archimedean triangular-norms. (C) 1998 Published by Elsevier Science B.V. All rights reserved.