I was reading the proof of Lemma 26.13.2. here and it seems they use the following fact, but I haven't been able to find a proof of it. Could anyone provide a reference/proof?
Let $X$ be a scheme and $x,x'\in X$ points. Suppose that $x\in\overline{\{x'\}}$, this is, $x'$ is a generalisation if $x$. If $U\subseteq X$ is an affine open neighbourhood of $x$, then $x'\in U$.
This is just a general topological result. If $X$ is a topological space and $Y \subset X$ then $x \in \bar{Y}$ if and only if we have $U \cap Y \neq \emptyset$ whenever $U$ is an open neighbourhood of $x$.