  In this paper we consider well-posedness properties of vector optimization
problems with objective function $f: X \to Y$ where $X$ and $Y$ are Banach
spaces and $Y$ is partially ordered by a closed convex pointed cone with
nonempty interior. The vector well-posedness notion considered in this paper is
the one due to Dentcheva and Helbig, which is a natural extension of Tykhonov
well-posedness for scalar optimization problems. When a scalar optimization
problem is considered it is possible to prove that under some assumptions the
set of functions for which the related optimzation problem is well-posed is
dense or even more in "big" i.e. contains a dense $G_{\delta}$ set (these
results are called genericity results). The aim of this paper is to extend
these genericity results to vector optimization problems.
