Lemma 28.2.2. Let $X$ be a scheme and let $E \subset X$ be a locally constructible subset. Let $\xi \in X$ be a generic point of an irreducible component of $X$.
If $\xi \in E$, then an open neighbourhood of $\xi $ is contained in $E$.
If $\xi \not\in E$, then an open neighbourhood of $\xi $ is disjoint from $E$.
Comment #3440 by Takumi Murayama on
Comment #3495 by Johan on