Abstract

We study modules over the ring ˜ C of complex generalized numbers from a topological point of view, introducing the notions of ˜ C-linear topology and locally convex ˜ C-linear topology. In this context particular attention is given to completeness, continuity of ˜ C-linear maps and elements of duality theory for topological ˜ C-modules. As main examples we consider various Colombeau algebras of generalized functions. Key words: modules over the ring of complex generalized numbers, algebras of generalized functions, topology, duality theory

Citations