Definition:Topology on Étalé Space of Presheaf

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

Let $\FF$ be a presheaf of sets on $T$.

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

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

Also see

 * Definition:Section of Étalé Space