Mackey topology

Summary

The Mackey topology $\tau(X, Y)$ of a dual pair $(X, Y)$ is a topology on $X$. It is the topology of uniform convergence on the convex, balanced, weakly compact subsets of $Y$. By the Mackey–Arens theorem, it is the finest locally convex topology on $X$ whose continuous dual is $Y$. So, among all locally convex topologies with a given dual, the weak topology is the coarsest and the Mackey topology is the finest.