  In this work, we found a non trivial topology to achieve the controllability
for linear and nonlinear system in finite or infinite time horizon. We give
several examples illustrating this topologizing method for the controllability
results. We obtain by the way the controllability for the one dimensional
Schr\"odinger. We also apply this method to achieve the both controllability of
Korteweg-de Vries and Saint-Venant equations.
