Definition:Boundary (Topology)/Definition 4

Definition
Let $T = \struct {S, \tau}$ be a topological space.

Let $H \subseteq S$.

The boundary of $H$ consists of all the points in $H$ which are not in either the interior or exterior of $H$.

Thus, the boundary of $H$ is defined as:
 * $\partial H := H \setminus \paren {H^\circ \cup H^e}$

where:
 * $H^\circ$ denotes the interior of $H$
 * $H^e$ denotes the exterior of $H$.

Also known as
The boundary of a subset $H$ is also seen referred to as the frontier of $H$.

Also see

 * Equivalence of Definitions of Boundary