Sheaf of holomorphic functions

Definition

On an open subset in complex numbers

Suppose $U\subset \mathbb{C}$ is an open subset. The sheaf of holomorphic functions on $U$ is a sheaf of $\mathbb{C}$-algebras defined as follows:

• For every open subset $V\subset U$, the algebra is the $\mathbb{C}$-algebra of holomorphic functions on $V$
• The restriction maps are simply function restriction