Identity theorem for Riemann surfaces
From Wikipedia, the free 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.
[edit] Statement of the theorem
Let X and Y be Riemann surfaces, and let 
be holomorphic. Suppose that f | A = g | A for some subset 
that has a limit point, where 
denotes the restriction of f to A. Then f = g (on the whole of X).
