The Stacks project

Lemma 5.5.5. Let $X$ be a set. Given any collection $\mathcal{B}$ of subsets of $X$ there is a unique topology on $X$ such that $\mathcal{B}$ is a subbase for this topology.

Proof. By convention $\bigcap _\emptyset B = X $. Thus we can apply Lemma 5.5.2 to the set of finite intersections of elements from $\mathcal B$. $\square$

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