  We study dentable maps from a closed convex subset of a Banach space into a
metric space as an attempt of generalize the Radon-Nikod\'ym property to a
"less linear" frame. We note that a certain part of the theory can be developed
in rather great generality. Indeed, we establish that the elements of the dual
which are "strongly slicing" for a given uniformly continuous dentable function
form a dense $\mathcal{G}_\delta$ subset of the dual. As a consequence, the
space of uniformly continuous dentable maps from a closed convex bounded set to
a Banach space is a Banach space. However some interesting applications, as
Stegall's variational principle, are no longer true beyond the usual
hypotheses, sending us back to the classical case. Moreover, we study the
connection between dentability and approximation by delta-convex functions for
uniformly continuous functions. Finally, we show that the dentability of a set
is closely related with the dentability of delta-convex maps defined on it.
