Every closed immersion is a finite morphism. Can you give an example of quasi-projective varieties $X\subset Y$ such that inclusion $X\hookrightarrow Y$ is not finite? Same with Y projective?


Thanks!


**Edit:** Sorry this question is very simple, I made a mistake asking the question. For a corrected version, check out [this one.](https://mathoverflow.net/questions/17678/example-of-restriction-of-a-finite-morphism-which-is-not-finite)



Example of inclusion which is not a finite morphism
An open immersion is never finite unless it is also a closed immersion (for finite morphisms are proper). So you just need to take a non-empty open subset $X$ which is not a connected component in $Y$. 


