Open Set

Pub May 07, 2026 Up Jun 20, 2026

Definition 1. Let $X$ be a metric space and $Y \subseteq X$. $Y$ is open if

\[Y = \inter Y.\]

Proposition 1. Let $X$ be a metric space. If $\mathcal{S}$ is a set of open sets from $X$, then $\bigcap \mathcal{S}$ is open.