S. Cobza\c s
Antiproximinal sets in the Banach space $ c(X)$

Comment.Math.Univ.Carolinae 38,2 (1997) 247-253.

Abstract: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 $V$.

Keywords: antiproximinal sets, best approximation
AMS Subject Classification: 41A65