Exterior (Topology)

Definition

Let $(X,d)$ be a metric space and $A\subseteq X$. A point $x\in X$ is an exterior point of $A$ if it is an interior point of the complement $X-A$. The exterior of $A$ is denoted $\text{ext}(A)$. $\text{ext}(A)=(X-A{)}^{\circ }$

Properties

1. $\text{ext}(A)=X-\overline{A}$.
2. The metric space $X$ is partitioned into three disjoint sets: the interior $A^{\circ }$, the exterior $\text{ext}(A)$, and the boundary $\partial A$.