# Extended complex plane

From Encyclopedia of Mathematics

The complex -plane compactified by adding the point at infinity and written as . The exterior of any circle in , that, is, any set of the form , , becomes a neighbourhood of . The extended complex plane is the Aleksandrov compactification of the plane , and is both homeomorphic and conformally equivalent to the Riemann sphere. The spherical, or chordal, metric on is given by

#### References

[1] | A.I. Markushevich, "Theory of functions of a complex variable" , 1–2 , Chelsea (1977) (Translated from Russian) |

[2] | B.V. Shabat, "Introduction of complex analysis" , 1–2 , Moscow (1976) (In Russian) |

#### Comments

#### References

[a1] | J.B. Conway, "Functions of one complex variable" , Springer (1978) |

**How to Cite This Entry:**

Extended complex plane. E.D. Solomentsev (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Extended_complex_plane&oldid=12466

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098