Reminders on topological vector spaces
Examples in Topology II. Products Spaces, Vector Spaces, Sequence Spaces, Function Spaces, and Subset Spaces
Quizzed article REF: AF123 V1
Reminders on topological vector spaces
Examples in Topology II. Products Spaces, Vector Spaces, Sequence Spaces, Function Spaces, and Subset Spaces

Author : Jean-Charles PINOLI

Publication date: October 10, 2018, Review date: May 7, 2021 | Lire en français

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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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