Definition:Open Subscheme

Definition
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 $U$.

Also see

 * Open Subscheme is Scheme
 * Definition:Closed Subscheme