Let $X$ be a metric space and $Y \subseteq X$. $Y$ is open if
\[Y = \inter Y.\]
Let $X$ be a metric space. If $\mathcal{S}$ is a set of open sets from $X$, then $\bigcap \mathcal{S}$ is open.
Let $X$ be a metric space and $Y \subseteq X$. $Y$ is open if
\[Y = \inter Y.\]
Let $X$ be a metric space. If $\mathcal{S}$ is a set of open sets from $X$, then $\bigcap \mathcal{S}$ is open.