# geometry ag.algebraica – Sections of pulleys in boundary spaces

Leave $${U _ { nu} } _ { nu in I}$$ To be an inverse system of topological spaces on a set of filtered indexes. $$I$$ With continuous transition maps.

Leave $$A$$ To be a sheaf of abelian groups in the topological space. $$U = varprojlim U _ { nu}$$ and call $$U _ { nu} subset U$$ the preimage of $$U _ { nu}$$ in $$U$$ through the map $$U a U _ { nu}$$ from the inverse limit.

When we have
$$A (U) = varinjlim A (U _ { nu})$$
for each sheaf of abelian groups $$A$$? We always have this when $$A$$ It is the constant sheaf with values ​​in the Abelian group. $$A$$?

Yes $$U$$ It is compact Hausdorff this is true.

It is true when each $$U _ { nu}$$ it's even a smooth variety, the transition maps are local diffeomorphisms, but $$U$$ Is not it necessarily compact?