Let $X$ be a metric space and $Y\subseteq X$. $Y$ is closed if $X\setminus Y$ is open.
Let $X$ be a metric space. If $\mathcal{S}$ is a collection of closed sets from $X$, then $\bigcap\mathcal{S}$ is closed.
Let $X$ be a metric space and $Y\subseteq X$. $Y$ is closed if $X\setminus Y$ is open.
Let $X$ be a metric space. If $\mathcal{S}$ is a collection of closed sets from $X$, then $\bigcap\mathcal{S}$ is closed.