In mathematics, in the branch of complex analysis, a holomorphic function on an open subset of the complex plane is called univalent if it is injective.

Examples

is injective.

Basic properties

are two open connected sets in the complex plane, and

is surjective is invertible is also holomorphic. More, one has by the chain rule

Comparison with real functions

For real analytic functions, unlike for complex analytic (that is, holomorphic) functions, these statements fail to hold. For example, consider the function

is a primitive cube root of unity).

See also

Note

References

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