extended boundary

Definition.

Suppose that $ℂ$ is the complex plane and $G\subset ℂ$. The extended boundary of $G$ denoted ${\partial }_{\mathrm{\infty }}G$ is defined asthe boundary of $G$ plus the point at infinity if in fact $G$ is unbounded.

The extended boundary of $G$ is really the boundary of $G$in the extended complex plane (the one-pointcompactification of $ℂ$).