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In approximation theory, a Haar space or Chebyshev space is a finite-dimensional subspace V of $${\displaystyle {\mathcal {C}}(X,\mathbb {K} )}$$, where X is a compact space and $$\mathbb K$$ 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 V that approximates f "best", i.e. with minimum distance to f in supremum norm.[1]

References

Shapiro, Harold (1971). Topics in Approximation Theory. Springer. pp. 19–22. ISBN 3-540-05376-X.