Open Set

OPN#DEF. Open Set.

Let $X$ be a metric space and $Y\subseteq X$. $Y$ is open if

\[Y = \inter Y.\]

OPN#PROP-U.

Let $X$ be a metric space. If $\mathcal{S}$ is a collection of open sets from $X$, then $\bigcap\mathcal{S}$ is open.