Definition 1. (a) A set E u is said to be a topological vector space (or, in short, a TVS) over a given field K, if E u as a pointset is a topological space and a vector space over K such that the mappings: $$\begin{gathered} (x,y) \to x + y, \hfill \\ (\lambda ,x) \to \lambda x \hfill \\ \end{gathered}$$ are continuous in both variables together for x, y ∈ E and λ ∈ K.