Exercise 109.42.1. Let $X = \mathbf{R}$ with the usual Euclidean topology. Using only formal properties of cohomology (functoriality and the long exact cohomology sequence) show that there exists a sheaf $\mathcal{F}$ on $X$ with nonzero $H^1(X, \mathcal{F})$.

Comment #4591 by Théo de Oliveira Santos on

Very minor typo: Euclidian

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