Let $f : X \to Y$ be an open faithfully flat morphism of schemes. In the text I'm reading (Angelo Vistoli's notes on descent) it is claimed that then every point $x \in X$ admits an open neighorhood $U$ such that $f(U)$ is open and the morphism $U \to f(U)$ is quasi-compact. The latter is one of the possible definitons of a fpqc morphism. However, I don't understand at all why $U \to f(U)$ should be quasi-compact.

This is needed to prove that the fpqc topology is finer than the fppf topology.