  The 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.
