Geodesic
Some theorems on Chebyshev sets
Matematičeskie zametki, Tome 11 (1972) no. 2, pp. 135-144 
L. P. Vlasov. Some theorems on Chebyshev sets. Matematičeskie zametki, Tome 11 (1972) no. 2, pp. 135-144. http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a1/
@article{MZM_1972_11_2_a1,
     author = {L. P. Vlasov},
     title = {Some theorems on {Chebyshev} sets},
     journal = {Matemati\v{c}eskie zametki},
     pages = {135--144},
     year = {1972},
     volume = {11},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a1/}
}
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UR  - http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the class of $\delta$-suns which is used in the study of Chebyshev sets. We give sufficient conditions for a set to be a $\delta$-sun. We prove that, in a uniformly smooth Banach space, a weakly closed Chebyshev set is convex.