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Rigidity of the topological dual of spaces of formal series with respect to product topologies

Rigidity of the topological dual of spaces of formal series with respect to product topologies

Even in spaces of formal power series is required a topology in order to legitimate some operations, in particular to compute infinite summations. Many topologies can be exploited for different purposes. Combinatorists and algebraists may think to usual order topologies, or the product topology induced by a discrete coefficient field, …