Definition:Topology on Étalé Space of Presheaf

Definition
Let $T = \struct {S, \tau}$ be a topological space.

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

Let $\map {\operatorname {\acute Et} } {\mathcal F}$ be its étalé space.

The topology on $\map {\operatorname {\acute Et} } {\mathcal F}$ is the final topology with respect to the sections associated to elements of $\map {\mathcal F} U$ with $U \subseteq S$ open.

Also see

 * Definition:Section of Étalé Space