= Identity theorem for Riemann surfaces
{wiki=Identity_theorem_for_Riemann_surfaces}
The Identity Theorem for Riemann surfaces is a result in complex analysis that concerns holomorphic functions defined on Riemann surfaces, which are essentially one-dimensional complex manifolds. The theorem states that if two holomorphic functions defined on a connected Riemann surface agree on a set that has a limit point within that surface, then the two functions must be equal everywhere on the connected component of that Riemann surface.
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