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We study modules over the ring $\widetilde{\mathbb{C}}$ of complex generalized numbers from a topological point of view, introducing the notions of $\widetilde{\mathbb{C}}$ -linear topology and locally convex $\widetilde{\mathbb{C}}$ -linear topology. In this context particular attention is given to completeness, continuity of $\widetilde{\mathbb{C}}$ -linear maps and elements of duality theory for topological $\widetilde{\mathbb{C}}$ -modules. As main examples we consider various Colombeau algebras of generalized functions.
Acta Applicandae Mathematicae – Springer Journals
Published: Apr 29, 2005
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