Uniqueness theorem - Revision history

Vipul: 4 revisions

2008-05-18T19:19:20Z

4 revisions

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Vipul: /* For Riemann surfaces */

2008-05-03T21:57:29Z

For Riemann surfaces

← Older revision		Revision as of 21:57, 3 May 2008
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	===For Riemann surfaces===		===For Riemann surfaces===

	{~~{fillin}~~}		Suppose <math>M</math> is a [[Riemann surface]]. In other words, <math>M</math> is a connected surface with an atlas of coordinate charts having conformal transition maps. Then, if <math>f,g: M \to \mathbb{C}</math> are [[holomorphic function]]s, we either have <math>f \equiv g</math>, or the set of points where <math>f = g</math>, is a discrete closed subset.

	==Related facts==		==Related facts==

	* [[Holomorphic function is determined by its germ]]: An easy corollary of the uniqueness theorem		* [[Holomorphic function is determined by its germ]]: An easy corollary of the uniqueness theorem

Vipul at 19:28, 26 April 2008

2008-04-26T19:28:25Z

← Older revision		Revision as of 19:28, 26 April 2008
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			{{basic fact}}
	==Statement==		==Statement==

Vipul at 19:27, 26 April 2008

2008-04-26T19:27:43Z

← Older revision		Revision as of 19:27, 26 April 2008
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	{{fillin}}		{{fillin}}

			==Related facts==

			* [[Holomorphic function is determined by its germ]]: An easy corollary of the uniqueness theorem

Vipul: New page: ==Statement== ===For domains in the complex numbers=== Suppose $U$ is a nonempty domain (open connected subset) of $\mathbb{C}$ . Then, given two maps $f,g:...$

2008-04-18T22:01:30Z

New page: ==Statement== ===For domains in the complex numbers=== Suppose <math>U</math> is a nonempty domain (open connected subset) of <math>\mathbb{C}</math>. Then, given two maps <math>f,g:...

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