  Given a cover $\mathcal{B}$ of a quasi-uniform space $Y$ we introduce a
concept of lower semicontinuity for multifunctions $F:X\to 2^Y$, called
$\mathcal{B}$-lsc. In this way, we get a common description of Vietoris-lsc,
Hausdorff-lsc, and bounded-Hausdorff-lsc as well. Further, we examine
set-theoretical and vector operations on such multifunctions. We also point out
that the convex hull of Hausdorff-lsc multifunctions need not to be
Hausdorff-lsc except the case where the range space is locally convex.
