Picard's little theorem: Difference between revisions

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(New page: ==Statement== The range of a nonconstant entire function (holomorphic function on the whole of <math>\mathbb{C}</math>) can miss at most one point. Equivalently, any entire function ...)
 
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{{basic fact}}
==Statement==
==Statement==



Revision as of 18:58, 26 April 2008

This article gives the statement, and possibly proof, of a basic fact in complex analysis.
View a complete list of basic facts in complex analysis

Statement

The range of a nonconstant entire function (holomorphic function on the whole of ) can miss at most one point.

Equivalently, any entire function whose range omits two points is a constant.

Relation with other facts

Stronger facts

Weaker facts

Other related facts