Let $X\subseteq \mathbb{P}^n(\mathbf{C})$ be a quasi-projective variety.


Q: Is $X$ necessarily quasi-compact in the Zariski topology (if yes then how to prove it)?



Does quasi-projective imply quasi-compact (in the Zariski topology)?
Say, any subset of a Noetherian topological space is quasi-compact with respect to the induced topology.


