Diametral dimensions of Fréchet spaces
Volume 234 / 2016
Studia Mathematica 234 (2016), 271-280
MSC: 46A04, 46A11, 46A63.
DOI: 10.4064/sm8597-6-2016
Published online: 29 August 2016
Abstract
The diametral dimension is an important topological invariant in the category of Fréchet 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, Pełczyński, and Rolewicz at least for nuclear Fréchet spaces. Moreover, we clarify the relation between an invariant recently introduced by Terzioğlu and the by now classical condition $(\overline \Omega )$ of Vogt and Wagner.
