Extended complex plane

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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


[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)



[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:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098