Suppose $f:X\to Y$ is a dominant morphism between varieties such that $k(Y)$ is a finite field extension of $k(X)$, $S\varsubsetneqq X$ is a proper closed subset (subvariety) of $X$. Is it always true that $\overline{f(S)}\ne Y$?
2026-03-27 14:02:07.1774620127
Given dominant morphism between irreducible varieties, prove that image of a proper closed subset is not dense.
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