Definition:Weakly Closed Set

Definition
Let $K$ be a topological field.

Let $X$ be a topological vector space with weak topology $w$.

Let $C \subseteq X$.

We say that $C$ is weakly closed (or $w$-closed) in $X$ $C$ is closed in $\struct {X, w}$.

That is, $U = X \setminus C$ is weakly open.