I read the following result in an article.

Let $X$ be a regular space. Let $\mathcal{M}$ be free closed ultrafilter on $X$. Set $\mathcal{U=}\left\{ U:U\text{ is open and there exists a }F\in \mathcal{M}\text{ such that }F\subset U\right\} $. $\mathcal{U% }$ is contained in an open ultrafilter $\mathcal{W}$. By regularity, $\bigcap \overline{\mathcal{W}}=\emptyset $.

Why the regularity implies $\bigcap \overline{\mathcal{W}}=\emptyset $?