Good cover (algebraic topology)

The concept was introduced by André Weil in 1952 for differentiable manifolds, demanding the

However, for the purposes of computing the Čech cohomology it suffices to have a more relaxed definition of a good cover in which all intersections of finitely many open sets have contractible connected components.

This follows from the fact that higher derived functors can be computed using acyclic resolutions.

The more relaxed definition of a good cover allows us to do this using only three open sets.

A cover can be formed by choosing two diametrically opposite points on the sphere, drawing three non-intersecting segments lying on the sphere connecting them and taking open neighborhoods of the resulting faces.