Consider the sets $Y_{k}:=\{y\in Y\mid |f^{-1}(y)|\leq k\}$, where $f:X\to Y$ is a flat quasi-finite morphism between smooth irreducible affine varieties and $k$ a natural number. Are these sets $Y_{k}$ closed in $Y$?
2026-03-26 17:34:47.1774546487
Closed sets flat morphism
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