Completely distributive enriched categories are not always continuous

In contrast to the fact that every completely distributive lattice is necessarily continuous in the sense of Dana Scott, it is shown that complete distributivity of a category enriched over the closed category obtained by endowing the unit interval with a continuous t-norm does not imply continuity in general. Necessary and sufficient conditions for the implication are presented in terms of the structure of the table of truth-values --- the unit interval together with the continuous t-norm.