Abstract
For a Banach space, having a copy of $c_0$ is a strong way of
failing the Radon--Nikodym property. We show how the dentability can be
modified with a suitable notion of diameter in order to recognize some
relationships with $c_0$. On the other hand, we prove a Bourgain-like
characterization of spaces with no copy of $c_0$. This is a joint work with A.
Pérez, JFA 2013 and RACSAM 2016.