Lemma 29.47.9. Let $X$ be a scheme. The following are equivalent

$X$ is seminormal,

$X$ is equal to its own seminormalization, i.e., the morphism $X^{sn} \to X$ is an isomorphism,

if $\pi : Y \to X$ is a universal homeomorphism inducing isomorphisms on residue fields with $Y$ reduced, then $\pi $ is an isomorphism.

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