Lemma 7.47.7. Let $\mathcal{C}$ be a category. Let $J$ be a topology on $\mathcal{C}$. Let $U \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$.

Finite intersections of elements of $J(U)$ are in $J(U)$.

If $S \in J(U)$ and $S' \supset S$, then $S' \in J(U)$.

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