Topological structures in Colombeau algebras: topological ℂ̃-modules and duality theory Claudia Garetto 2134/17311 https://repository.lboro.ac.uk/articles/journal_contribution/Topological_structures_in_Colombeau_algebras_topological_-modules_and_duality_theory/9387350 We study modules over the ring ℂ̃ of complex generalized numbers from a topological point of view, introducing the notions of ℂ̃-linear topology and locally convex ℂ̃-linear topology. In this context particular attention is given to completeness, continuity of ℂ̃-linear maps and elements of duality theory for topological ℂ̃-modules. As main examples we consider various Colombeau algebras of generalized functions. © Springer 2005. 2015-04-20 11:17:24 Algebras of generalized functions Duality theory Modules over the ring of complex generalized numbers Topology Mathematical Sciences not elsewhere classified