Haar space

In approximation theory, a Haar space or Chebyshev space is a finite-dimensional subspace [math]\displaystyle{ V }[/math] of [math]\displaystyle{ \mathcal C(X, \mathbb K) }[/math], where [math]\displaystyle{ X }[/math] is a compact space and [math]\displaystyle{ \mathbb K }[/math] either the real numbers or the complex numbers, such that for any given [math]\displaystyle{ f \in \mathcal C(X, \mathbb K) }[/math] there is exactly one element of [math]\displaystyle{ V }[/math] that approximates [math]\displaystyle{ f }[/math] "best", i.e. with minimum distance to [math]\displaystyle{ f }[/math] in supremum norm.