Let $X\subseteq \mathbb{P}^n(\mathbf{C})$ be a quasiprojective variety.
Q: Is $X$ necessarily quasicompact in the Zariski topology (if yes then how to prove it)?
Let $X\subseteq \mathbb{P}^n(\mathbf{C})$ be a quasiprojective variety. Q: Is $X$ necessarily quasicompact in the Zariski topology (if yes then how to prove it)? 


Say, any subset of a Noetherian topological space is quasicompact with respect to the induced topology. 

