Let X be a topological space having an open cover U1,..., Un with the property that all k-fold intersections U;, n..NUig are either empty or contractible for all k = 1, .. ,n (this is an example of an acyclic cover). (a) Show that H;(X) = 0 for i >n 1. (b) For each n, construct an example of such a space X having nonzero Hn-2(X).

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