Definition 1

A locally convex topology $\mathscr{T}$ on E is said to be compatible with the duality between E and F if $d_B$ is a bijection from F onto the dual of the locally convex space obtained by assigning the topology $\mathscr{T}$ to E.

If there exists one such topology $\mathscr{T}$, the mapping $d_B$ is injective, that is to say, the duality between E and F is separating in F (II, p. 41).