Definition:Exterior (Topology)

Definition
Let $$T$$ be a topological space.

Let $$H \subseteq T$$.

The exterior of $$H$$ is the complement of the closure of $$H$$ in $$T$$.

Alternatively, the exterior of $$H$$ is the interior of the complement of $$H$$ in $$T$$.

It can be denoted:
 * $$\operatorname{Ext} \left({H}\right)$$
 * $$H^e$$

Also see

 * Equivalence of Definitions of Exterior