In mathematics, an open cover of a topological space is a family of open subsets such that is the union of all of the open sets. A good cover is an open cover in which all sets and all non-empty intersections of finitely-many sets are contractible. The concept was introduced by André Weil in 1952 for differentiable manifolds, demanding the to be differentiably contractible.A modern version of this definition appears in .
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