Every continuous function on [a,b] is uniformly approximable by polynomials. Stone-Weierstrass generalisation: any subalgebra of C(K, ℝ) that contains constants and separates points is dense. Foundation of approximation theory.
Every continuous function on [a,b] is uniformly approximable by polynomials. Stone-Weierstrass generalisation: any subalgebra of C(K, ℝ) that contains constants and separates points is dense. Foundation of approximation theory.