Closest Point Property
Result
Suppose $X$ is a complete inner product space,
$A \subset X$ closed and convex, and $x \in X$.
There exists a unique $z \in X$ satisfying
\[ d(z, x) = \inf_{y \in A} d(y, x). \]
\[ d(z, x) = \inf_{y \in A} d(y, x). \]