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?
Closed morphism between schemes of finite type over a field induces a closed map between varieties?
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algebraic-geometry