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 $T$.

Notation
The exterior of $H$ can be denoted:


 * $\operatorname{Ext} \left({H}\right)$
 * $H^e$

The first is regarded by some as cumbersome, but has the advantage of being clear.

$H^e$ is neat and compact, but has the disadvantage of being relatively obscure.

On this website, $H^e$ is the notation of choice.

Also see

 * Equivalence of Definitions of Exterior