  In this note we review some results on the transversality conditions for a
smooth Fredholm map $f: X \times (0,T) \to Y$ between two Banach spaces $X,Y$.
These conditions are well-known in the realm of bifurcation theory and commonly
accepted as "generic". Here we show that under the transversality assumptions
the sections $C(t)=\{x:f(x,t)=0\}$ of the zero set of $f$ are discrete for
every $t\in (0,T)$ and we discuss a somehow explicit family of perturbations of
$f$ along which transversality holds up to a residual set.
  The application of these results to the case when $f$ is the $X$-differential
of a time-dependent energy functional $E:X\times (0,T)\to R$ and $C(t)$ is the
set of the critical points of $E$ provides the motivation and the main example
of this paper.
