  We provide a unified, elementary, topological approach to the classical
results stating the continuity of the complex roots of a polynomial with
respect to its coefficients, and the continuity of the coefficients with
respect to the roots. In fact, endowing the space of monic polynomials of a
fixed degree $n$ and the space of $n$ roots with suitable topologies, we are
able to formulate the classical theorems in the form of a homeomorphism.
Related topological facts are also considered.
