Geodesic
Weak continuity of metric projections
Matematičeskie zametki, Tome 22 (1977) no. 3, pp. 345-356 
V. S. Balaganskii. Weak continuity of metric projections. Matematičeskie zametki, Tome 22 (1977) no. 3, pp. 345-356. http://geodesic.mathdoc.fr/item/MZM_1977_22_3_a3/
@article{MZM_1977_22_3_a3,
     author = {V. S. Balaganskii},
     title = {Weak continuity of metric projections},
     journal = {Matemati\v{c}eskie zametki},
     pages = {345--356},
     year = {1977},
     volume = {22},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_3_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A necessary and sufficient condition is found for weak continuity of a metric projection onto a finite-dimensional subspace in $l_p$ ($1). 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.