Sheaf of holomorphic functions: Difference between revisions
(New page: ==Definition== ===On an open subset in complex numbers=== Suppose <math>U \subset \mathbb{C}</math> is an open subset. The '''sheaf of holomorphic functions''' on <math>U</math> is a she...) |
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===On an open subset in complex numbers=== | ===On an open subset in complex numbers=== | ||
Suppose <math>U \subset \mathbb{C}</math> is an open subset. The '''sheaf of holomorphic functions''' on <math>U</math> is a sheaf of <math>\C</math>-algebras defined as follows: | Suppose <math>U \subset \mathbb{C}</math> is an open subset. The '''sheaf of holomorphic functions''' on <math>U</math> is a sheaf of <math>\mathbb{C}</math>-algebras defined as follows: | ||
* For every open subset <math>V \subset U</math>, the algebra is the <math>\mathbb{C}</math>-algebra of holomorphic functions on <math>V</math> | * For every open subset <math>V \subset U</math>, the algebra is the <math>\mathbb{C}</math>-algebra of holomorphic functions on <math>V</math> | ||
* The restriction maps are simply function restriction | * The restriction maps are simply function restriction | ||
Revision as of 23:36, 18 April 2008
Definition
On an open subset in complex numbers
Suppose is an open subset. The sheaf of holomorphic functions on is a sheaf of -algebras defined as follows:
- For every open subset , the algebra is the -algebra of holomorphic functions on
- The restriction maps are simply function restriction