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.
Mots-clés :
diametral dimension important topological invariant category chet spaces which has distinguish types stein manifolds introduce variants classical definition order solve old conjecture bessaga mityagin czy ski rolewicz least nuclear chet spaces moreover clarify relation between invariant recently introduced terzio classical condition overline omega vogt wagner
@article{10_4064_sm8597_6_2016,
author = {Lo{\"\i}c Demeulenaere and Leonhard Frerick and Jochen Wengenroth},
title = {Diametral dimensions of {Fr\'echet} spaces},
journal = {Studia Mathematica},
pages = {271--280},
year = {2016},
volume = {234},
number = {3},
doi = {10.4064/sm8597-6-2016},
language = {fr},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm8597-6-2016/}
}
TY - JOUR
AU - Loïc Demeulenaere
AU - Leonhard Frerick
AU - Jochen Wengenroth
TI - Diametral dimensions of Fréchet spaces
JO - Studia Mathematica
PY - 2016
SP - 271
EP - 280
VL - 234
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4064/sm8597-6-2016/
DO - 10.4064/sm8597-6-2016
LA - fr
ID - 10_4064_sm8597_6_2016
ER -
