\begin{definition}[Definition:Quasi-Compact Morphism of Schemes]
Let $\struct {X, \OO_X}$ and $\struct {Y, \OO_Y}$ be schemes.
Let $f : \struct {X, \OO_X} \to \struct {Y, \OO_Y}$ be a morphism of schemes.
$f$ is '''quasi-compact''' {{iff}} for all quasi-compact open subsets $U \subset Y$, the set $\map {f^{-1} } U \subset X$ is quasi-compact.
Category:Definitions/Algebraic Geometry
Category:Definitions/Schemes
\end{definition}