Let $V$ be a real locally convex space. Let $F : V \to R$. Are the following equivalent?
(a) $\{ u \in V : F(u) \leq a \}$ is closed for any $a \in R$.
(b) $\liminf_{n} F(u_n) \geq F(u)$ whenever $u_n \to u$.
(I see (a) $\Rightarrow$ (b) but not the converse.)