en>Brad7777: /* See also */ added category types of functions

2011-11-12T10:59:20Z

See also: added category types of functions

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In [[mathematics]], the '''identity theorem for [[Riemann surface]]s''' 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 <math>X</math> and <math>Y</math> be Riemann surfaces, let X be connected, and let <math>f : X \to Y</math> be holomorphic. Suppose that <math>f|_{A} = g|_{A}</math> for some subset <math>A \subseteq X</math> that has a limit point, where <math>f|_{A} : A \to Y</math> denotes the [[restriction]] of <math>f</math> to <math>A</math>. Then <math>f = g</math> (on the whole of <math>X</math>).

== References ==
* {{Citation | last1=Forster | first1=Otto | author1-link= Otto Forster | title=Lectures on Riemann surfaces | publisher=Springer Verlag | location=New-York | series=Graduate Text in Mathematics | isbn=0-387-90617-7 | year=1981 | volume=81 | page=6}}

{{DEFAULTSORT:Identity Theorem For Riemann Surfaces}}
[[Category:Theorems in complex analysis]]
[[Category:Riemann surfaces]]

Radonifying function - Revision history

en>Brad7777: /* See also */ added category types of functions