Definition:Boundary (Topology)/Definition 3

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

Let $H \subseteq S$.

The boundary of $H$ is the intersection of the closure of $H$ with the closure of the complement of $H$ in $T$:


 * $\partial H = H^- \cap \paren {\overline H}^-$

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