2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160435The celebrated and famous Weierstrass approximation theorem characterizes the set of continuous functions on a compact interval via uniform approximation by algebraic polynomials. This theorem is the first significant result in Approximation Theory of one real variable and plays a key role in the development of General Approximation Theory. Our aim is to investigate some new results relative to such theorem, to present a history of the subject, and to introduce some open problems.16 pagesClassical Analysis and ODEsFunctional Analysis41, 41A10, 43A32, 47A56text