Geodesic
On Selections from the Best $n$-Nets
Matematičeskie zametki, Tome 104 (2018) no. 5, pp. 694-699

Voir la notice de l'article provenant de la source Math-Net.Ru

The discontinuity of any selection from a best $n$-net for $n\ge 2$ in an arbitrary not strictly convex Banach space is proved. It is also proved that there is no Lipschitz selection on an arbitrary Banach space of dimension at least 2 whose unit sphere contains an attainable point of smoothness.
Keywords: Banach space, selection, best $n$-net, Chebyshev center. 
@article{MZM_2018_104_5_a5,
     author = {Yu. Yu. Druzhinin},
     title = {On {Selections} from the {Best} $n${-Nets}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {694--699},
     publisher = {mathdoc},
     volume = {104},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_5_a5/}
}
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Yu. Yu. Druzhinin. On Selections from the Best $n$-Nets. Matematičeskie zametki, Tome 104 (2018) no. 5, pp. 694-699. http://geodesic.mathdoc.fr/item/MZM_2018_104_5_a5/