On pg 282 Prop 5.68 Rotman makes the following construction given a presheaf $P$ of abelian groups over a space $X$. The construction is as follows: For $P^{et}:= (E^{et}, p^{et},X)$.
I am struggling in understanding the topolgoy defined on $E^{et}$.
There are two statements, on -2 line of pg 282,
How is lemma 5.30 (ii) applied? Why is $\langle \tau, W \rangle \subseteq \langle \sigma, U \rangle \cap \langle \sigma' , U' \rangle $?
Lastly
Why is this the coarsest topology on $E$ making all sections continuous. What are the sections?