2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71751We study modules over the ring $\widetilde{\C}$ of complex generalized numbers from a topological point of view, introducing the notions of $\widetilde{\C}$-linear topology and locally convex $\widetilde{\C}$-linear topology. In this context particular attention is given to completeness, continuity of $\widetilde{\C}$-linear maps and elements of duality theory for topological $\widetilde{\C}$-modules. As main examples we consider various Colombeau algebras of generalized functionsGeneral Topology46F30, 13J99, 46A20text