\begin{definition}[Definition:Open Subscheme]
Let $\struct {X, \OO_X}$ be a scheme.
Let $U \subset X$ be an open subset.
Then the '''open subscheme''' defined by $U$ is the restriction $\struct {U, \OO_X {\restriction_U}}$ of $\struct {X, \OO_X}$ to $U$.
\end{definition}