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Let $X$ be a topological space and $\mathcal{F}$ be a sheaf of commutative topological groups on $X$. I am interested in the following question: Is there a natural way to introduce topology on $H^i(X,...

Disclaimer: This is a cross-listing of a math.stackexchange post. While not research level, after a week of no response, I figured I would ask it here. For a topological group $G$ and a topological ...