Identity theorem for Riemann surfaces - Alchetron, the free social encyclopedia

In mathematics, the identity theorem for Riemann surfaces is a theorem that states that a holomorphic function is completely determined by its values on any subset of its domain that has a limit point.

Statement of the theorem

Let X and Y be Riemann surfaces, let X be connected, and let f : X → Y be holomorphic. Suppose that f | A = g | A for some subset A ⊆ X that has a limit point, where f | A : A → Y denotes the restriction of f to A . Then f = g (on the whole of X ).

References

Identity theorem for Riemann surfaces Wikipedia

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