Lemma 17.3.2.label Let $\dpn{E, F}{\lambda}$ be a duality over $K \in \RC$, $\mathcal{T}\subset 2^{E}$ be a locally convex topology consistent with $\dpn{E, F}{\lambda}$, then for any $A \subset E$ convex, the $\mathcal{T}$-closure of $A$ and the $\sigma(E, F)$-closure of $A$ coincide.