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Explain where we use Hausdorff property
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aisejohan committed Jun 8, 2020
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Expand Up @@ -2645,6 +2645,7 @@ \section{Cohomology on Hausdorff quasi-compact spaces}
such that $h_{i_0 \ldots i_n}|_{W_{i_0 \ldots i_n, k}}$
lifts to a section of $\mathcal{G}$ over $W_{i_0 \ldots i_n, k}$.
By Topology, Lemma \ref{topology-lemma-refine-covering}
(this is where we use the assumption that $X$ is hausdorff and quasi-compact)
we can choose an open covering $\mathcal{V} : X = \bigcup_{j \in J} V_j$
and $\alpha : J \to I$ such that $V_j \subset U_{\alpha(j)}$
(it is a refinement) and such that for all $j_0, \ldots, j_n \in J$
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