Boundary Point

A point which is a member of the Closure of a given set $S$ and the Closure of its complement set. If $A$ is a subset of $\Bbb{R}^n$, then a point ${\bf x} \in \Bbb{R}^n$ is a boundary point of $A$ if every Neighborhood of ${\bf x}$ contains at least one point in $A$ and at least one point not in $A$.

See also Boundary