Geodesic
Chebyshev centers in hyperplanes of $c_0$
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 4, pp. 721-729.

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We give a full characterization of the closed one-codimensional subspaces of $c_0$, in which every bounded set has a Chebyshev center. It turns out that one can consider equivalently only finite sets (even only three-point sets) in our case, but not in general. Such hyperplanes are exactly those which are either proximinal or norm-one complemented.
Classification : 41A65, 46B20, 46B25
Keywords: Chebyshev centers; proximinal hyperplanes; space $c_0$ 
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     title = {Chebyshev centers in hyperplanes of $c_0$},
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Veselý, Libor. Chebyshev centers in hyperplanes of $c_0$. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 4, pp. 721-729. http://geodesic.mathdoc.fr/item/CMJ_2002__52_4_a4/