Good cover

In mathematics, an open cover of a topological space ${\displaystyle X}$ is a family of open subsets such that ${\displaystyle X}$ is the union of all of the open sets. In algebraic topology, an open cover is called a good cover if all open sets in the cover and all intersections of finitely many open sets, ${\displaystyle U_{\alpha _{1}\ldots \alpha _{n}}=U_{\alpha _{1}\ldots \alpha _{n-1}}\cap U_{\alpha _{n}}}$, are contractible (Petersen 2006).

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