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