Continuous dual of a weak-star topology
= Continuous dual of a weak-star topology
{title2=$(X^*,\sigma(X^*,X))'=J_X(X)$}
A <linear functional> on $X^*$ is continuous for the <weak-star topology> exactly when it is evaluation at an element of $X$. Continuity makes it vanish on the common kernel of finitely many evaluations, so it is a linear combination of those evaluations. The <canonical embedding into the bidual> identifies this dual with $X$.