Definition:Topology on Étalé Space of Presheaf
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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.