Lemma 5.19.2. Let $X$ be a topological space.

1. Any closed subset of $X$ is stable under specialization.

2. Any open subset of $X$ is stable under generalization.

3. A subset $T \subset X$ is stable under specialization if and only if the complement $T^ c$ is stable under generalization.

Proof. Omitted. $\square$

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