Strong dual space

Summary

The strong dual space of a topological vector space $E$ is its continuous dual $E'$ with a certain topology. It is the topology of uniform convergence on the bounded subsets of $E$. For a normed space this is just the norm topology of the dual norm. The strong dual is the default topology on $E'$ in the theory of reflexivity. A locally convex space $E$ is reflexive when the canonical map from $E$ to the strong dual of its strong dual is a topological isomorphism.