  The diametral dimension is an important topological invariant in the category
of Frechet spaces which has been used, e.g., to distinguish types of Stein
manifolds. We introduce variants of the classical definition in order to solve
an old conjecture of Bessaga, Mityagin, Pelczynski, and Rolewicz at least for
nuclear Frechet spaces. Moreover, we clarify the relation between an invariant
recently introduced by Terzioglu and the by now classical condition $(\bar
\Omega)$ of Vogt and Wagner.
