Lemma 5.19.3. Let $T \subset X$ be a subset of a topological space $X$. The following are equivalent
$T$ is stable under specialization, and
$T$ is a (directed) union of closed subsets of $X$.
Lemma 5.19.3. Let $T \subset X$ be a subset of a topological space $X$. The following are equivalent
$T$ is stable under specialization, and
$T$ is a (directed) union of closed subsets of $X$.
Proof. Omitted. $\square$
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