# Example of inclusion which is not a finite morphism [closed]

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.

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## closed as no longer relevant by Harry Gindi, Gjergji Zaimi, Yemon Choi, Scott Morrison♦Mar 10 '10 at 2:06

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Yes I surely can. Is this homework? What did you try? – Kevin Buzzard Mar 9 '10 at 21:51
Oops... sorry. – Qing Liu Mar 9 '10 at 22:13
You really can't change the question like that. – Harry Gindi Mar 10 '10 at 0:38
Well, at least after you've already received an answer. – Harry Gindi Mar 10 '10 at 0:39
Should I delete and resubmit? – Paul Yuryev Mar 10 '10 at 0:39

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 $Y$.