Source: wikibot/stone-weierstrass-theorem

= Stone–Weierstrass theorem
{wiki=Stone–Weierstrass_theorem}

The Stone–Weierstrass theorem is a fundamental result in analysis that provides conditions under which a set of functions can approximate continuous functions on a compact space. It generalizes the Weierstrass approximation theorem, which specifically addresses polynomial functions. Here is a more formal statement of the theorem: Let \\( X \\) be a compact Hausdorff space, and let \\( C(X) \\) denote the space of continuous real-valued functions on \\( X \\).