Definition:Boundary (Topology)

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

Let $H \subseteq S$.

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

Also defined as
Some sources define the boundary of a subset as:
 * the set of elements of $S$ which can be approached from within $S$ and from outside $S$.

However, this definition is of little use without rigorous definitions of approach, inside and outside.

Consequently, such imprecise definitions are not used on.

Also see

 * Equivalence of Definitions of Boundary


 * Boundary is Intersection of Closure with Closure of Complement


 * Definition:Boundary (Geometry)