Boundary of a set ($\partial A=\overline{A}\setminus A^{\circ }$)

The boundary of a subset $A$ of a topological space consists of the points whose every neighborhood meets both $A$ and its complement. Equivalently, $\partial A=\overline{A}\setminus A^{\circ }$, where the bar denotes closure and the circle denotes interior.

The boundary of a planar domain $D$ is its boundary of a set. It is distinct from the boundary of a parametrizing interval: a curve can begin on $\partial D$ while all its positive-time points lie inside $D$.