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Identity theorem for Riemann surfaces
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Identity theorem for Riemann surfaces : ウィキペディア英語版
Identity theorem for Riemann surfaces
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 \to Y be holomorphic. Suppose that f|_ = g|_ for some subset A \subseteq X that has a limit point, where f|_ : A \to Y denotes the restriction of f to A. Then f = g (on the whole of X).

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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