Let K be a nonempty subset of a normed linear space X and let x $in$ X. An element k$_0$ in K satisfying $$mid$$</TEX>x - k$_0$$$mid$$</TEX> = d(x, K) := (equation omitted) $$mid$$</TEX>x - k$$mid$$</TEX> is called a best approximation to x from K. For any x $in$ X, the set of all best approximations to x from K is denoted by P$_K$(x) = {k $in$ K : $$mid$$</TEX> x - k $$mid$$</TEX> = d(x, K)}. (omitted)