Definition:Boundary (Topology)/Also defined as

Boundary in the context of Topology: Also defined as
Some sources define the boundary of a subset of a topological space $T = \struct {S, \tau}$ 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.