Definition:Topology on Étalé Space of Presheaf

Definition
Let $X$ be a topological space.

Let $\mathcal F$ be a presheaf of sets on $X$.

Let $\operatorname{\acute Et} \left({\mathcal F}\right)$ be its étalé space.

The topology on $\operatorname{\acute Et} \left({\mathcal F}\right)$ is the final topology with respect to the sections associated to elements of $\mathcal F \left({U}\right)$ with $U\subseteq X$ open.

Also see

 * Definition:Section of Étalé Space