# extended boundary

###### Definition.

Suppose that ${\mathbb{C}}$ is the complex plane and $G\subset{\mathbb{C}}$. The extended boundary of $G$ denoted $\partial_{\infty}G$ is defined as the 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-point compactification of ${\mathbb{C}}$).

## References

• 1 John B. Conway. . Springer-Verlag, New York, New York, 1978.
Title extended boundary ExtendedBoundary 2013-03-22 14:12:11 2013-03-22 14:12:11 jirka (4157) jirka (4157) 7 jirka (4157) Definition msc 30-00 msc 54-00 BoundaryInTopology