ABSTRACT
Marti introduces the notion of extensions of algebras. This chapter presents an extension principle which contains sufficient conditions for extending a map between two topological algebras to their respective extensions. This principle is the main tool to study differential equations with generalized data or operators. The chapter investigates functorial properties of the construction. The topologies given by the valuations and by the bounds, respectively, have the same base of neighborhoods of zero. The chapter investigates the functorial properties of the construction. It looks for which mappings from a seminormed space to another can be extended to mappings between the respective extensions of the initial spaces.
