Point of closure

Let $(X, \tau)$ - a topological-space.

Point $x \in X$ is a point of closure of a set $S \subset X$ if $$ \forall U(x) \in \tau \hookrightarrow U(x) \cap S \neq \varnothing $$

Note: Point of closure of $S$ is not necessarily belongs to $S$. See topological-closure