View source for Element of best approximation

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An element $u_0$ in a given set $F$ that is a [[best approximation]] to a given element $x$ in a [[metric space]] $X$, i.e. is such that
$$
\rho(u_0,x) = \inf \{ \rho(u,x) : x \in F \} \ .

This is a generalization of the classical concept of a [[polynomial of best approximation]]. The main questions concerning elements of best approximation are: their existence and uniqueness, their characteristic properties (see [[Chebyshev theorem]]), the properties of the operator that associates with each element $x \in X$ the set of elements of best approximation (see [[Metric projection]]; [[Approximately-compact set]]), and numerical methods for the construction of elements of best approximation.