On Selections from the Best n-Nets
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The discontinuity of any selection from a best n-net for n ≥ 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.
KeywordsBanach space selection best n-net Chebyshev center
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