Étale space of a presheaf
= Étale space of a presheaf
{title2=$\operatorname{Et}(P)=\coprod_{x\in X}P_x$}
The space of <germs> of a presheaf has basic opens given by the germs of one section over an open set. Projection to its base point is a local homeomorphism. Continuous sections of this projection give <sheafification>. For the <constant presheaf of sets>, the basic opens are $U\times\{t\}$, giving the ordinary product with a discrete fibre.