Let $(E,t)$ be a Hausdorff locally convex space. Either $(E,\sigma (E,E^{\text{'}}))$ or $(E^{\text{'}},\sigma (E^{\text{'}},E))$ is a $DF$-space iff $E$ is of finite dimension (THEOREM). This is the most general solution of the problem studied by Iyahen [2] and Radenovič [3].