Geodesic
Antiproximinal sets in the Banach space $c(X)$
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 2, pp. 247-253

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If $X$ is a Banach space then the Banach space $c(X)$ of all $X$-valued convergent sequences contains a nonvoid bounded closed convex body $V$ such that no point in $C(X)\setminus V$ has a nearest point in $V$.
Classification : 41A50, 41A65, 46B20, 46B99
Keywords: antiproximinal sets; best approximation 
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     title = {Antiproximinal sets in the {Banach} space $c(X)$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {247--253},
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Cobzaş, S. Antiproximinal sets in the Banach space $c(X)$. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 2, pp. 247-253. http://geodesic.mathdoc.fr/item/CMUC_1997__38_2_a4/