3
$\begingroup$

Let $X$(resp. $Y$) be a scheme of finite type over a field $k$. Let $f\colon X \rightarrow Y$ be a closed morphism. Let $X_0$(resp. $Y_0$) be the set of closed points of $X$(resp. $Y$). Then $f$ induces a map $f_0\colon X_0 \rightarrow Y_0$(right?). We consider $X_0$(resp. $Y_0$) as a subspace of $X$(resp. $Y$). Is $f_0$ a closed map?

1 Answers 1