\begin{definition}[Definition:Restriction of Ringed Space to Open Set]
Let $\struct {X, \OO_X}$ be a ringed space.
Let $U \subset X$ be an open subset.
Let $\OO_X {\restriction_U}$ denote the restriction of $\OO_X$ to $U$.
The '''restriction''' of $\struct {X, \OO_X}$ to $U$ is the pair $\struct {U, \OO_X {\restriction_U} }$.
\end{definition}