Kuratowski convergence of the efficient sets in the parametric linear vector semi-infinite optimization

In the space of whole linear vector semi-infinite optimization problems we consider the mappings putting into correspondence to each problem the set of efficient and weakly efficient points, respectively. We endow the image space with Kuratowski convergence and by means of the lower and upper semi-continuity of these mappings we prove generic well-posedness of the vector optimization problems. The connection between the continuity and some properties of the efficient sets is also discussed.