Stone-Weierstrass theorem
= Stone-Weierstrass theorem
{c}
{wiki=Stone–Weierstrass_theorem}
A point-separating real subalgebra of $C(X)$ that contains the constants is uniformly dense when $X$ is compact Hausdorff. Polynomial approximation of the square root makes its closure a lattice; finite maxima and minima then turn pointwise interpolation into uniform approximation.