ABSTRACT
The main aim of this section is to expose some basic facts related to complexifications of topological vector spaces and to continuous inverse algebras.
DEFINITION A.1 A topological vector space over K ∈ {R,C} is a vector space X over K equipped with a Hausdorff topology such that both the vector addition X×X → X, (x, y) 7→ x+y, and the scalar multiplicationK×X → X, (λ, x) 7→ λx, are continuous mappings.
