Lemma 29.28.4. Let $f : X \to S$ be a morphism of schemes. Let $n \geq 0$. Assume $f$ is locally of finite type. The set

\[ U_ n = \{ x \in X \mid \dim _ x X_{f(x)} \leq n\} \]

is open in $X$.

[IV Theorem 13.1.3, EGA]

Lemma 29.28.4. Let $f : X \to S$ be a morphism of schemes. Let $n \geq 0$. Assume $f$ is locally of finite type. The set

\[ U_ n = \{ x \in X \mid \dim _ x X_{f(x)} \leq n\} \]

is open in $X$.

**Proof.**
This is immediate from Algebra, Lemma 10.125.6
$\square$

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## Comments (2)

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