Let $X$ be a normed space and let $V \subset X$ be a hyperplane. Prove that if there exists a vector $x_0 \in X-V $ such that the set $P_V(x_0)$ is nonempty, than $V$ is a proximinal set in $X$.
2026-03-27 05:34:27.1774589667
Approximation Theory, Hyperplane, Proximinal Set
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