Topology and functoriality in -algebras. Application to singular differential problems

We show that a new definition of the asymptotic structure of the ( C , E , P )-algebras (which are a refinement of the Colombeau Generalized Algebras) allows to define a natural topology on them. Furthermore, this topology can be mixed with functorial aspects of the construction in order to give extension principles, which give powerful tools to solve singular differential problems in this framework.