Definition:Topology on Étalé Space of Presheaf

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

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

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 $U \subseteq S$ open.

Also see

 * Definition:Section of Étalé Space