Weak continuity of metric projections

A necessary and sufficient condition is found for weak continuity of a metric projection onto a finite-dimensional subspace in $l_p$ ($1<p\ne2$). A metric projection onto a boundedly compact set in $l_p$ is sequentially weakly upper semicontinueus. An example is given on a convex, compact set in $l_2$ onto which the metric projection is not weakly continuous.