1. Reminders on topological vector spaces
A topological vector space is any abstract vector space (Peano, 1888) equipped with a compatible topology. It was M. Fréchet (1902) who initiated the study of metrizable topologies on vector spaces.
The aim of this section is to present the links between general topology and topological algebra, with a particular focus on topological vector spaces.
1.1 General topological vector spaces
Definition (topological vector space (Kolmogorov, 1934) (von Neumann, 1935)). A topological vector space (topological vector space)
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Reminders on topological vector spaces
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