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I am misunderstanding something in Theorem 2.1.9 in Dimca’s Sheaves in Topology: Let $X$ be a real smooth manifold. Then the natural morphism from the constant sheaf to the de Rham complex $$\mathbb{R}...

Let $X$ be a smooth manifold (usually assumed to be paracompact). Let us denote by $\underline{\Omega}^{p,-\infty}_X$ the sheaf of real valued $p$-forms with distributional coefficients in the ...