Dual pair

Summary

A dual pair, or dual system, consists of two vector spaces and a bilinear form between them that separates points on both sides. It is the abstract framework of duality theory for locally convex spaces. The basic example is a Hausdorff locally convex space $E$ paired with its continuous dual $E'$ by $\langle x, f \rangle = f(x)$. Topologies such as the weak topology and the Mackey topology are defined from a dual pair alone.