Continuous dual of a weak topology
= Continuous dual of a weak topology
{title2=$(E,\sigma(E,F))'=F$}
For a <separated dual pair>, the continuous linear functionals for its <weak topology> are exactly evaluations by members of the paired space. Continuity bounds a functional on a neighbourhood defined by finitely many evaluations; scalar rescaling makes it vanish on their common kernel. It then factors through their finite-dimensional evaluation map and is a finite linear combination of them.