Topological invariants, diametral dimension, and one related question

Diametral dimension is a topological invariant for topological vector spaces which appears to
be useful to characterize some classical classes of locally convex spaces (Schwartz, nuclear spaces).
In this talk, we first introduce the notion of Kolmogorov's diameters to define the diametral
dimension of a topological vector space. We also consider some simple properties of these concepts.
Then, we focus on an open question concerning the equality of the diametral dimension with one
of its variants.