Haar space

In approximation theory, a Haar space or Chebyshev space is a finite-dimensional subspace ${\displaystyle V}$ of ${\displaystyle {\mathcal {C}}(X,\mathbb {K} )}$, where ${\displaystyle X}$ is a compact space and ${\displaystyle \mathbb {K} }$ either the real numbers or the complex numbers, such that for any given ${\displaystyle f\in {\mathcal {C}}(X,\mathbb {K} )}$ there is exactly one element of ${\displaystyle V}$ that approximates ${\displaystyle f}$ "best", i.e. with minimum distance to ${\displaystyle f}$ in supremum norm.^[1]