- #1
Euge
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Let ##X## be a topological space, and let ##\mathscr{F}## be a sheaf on ##X##. Show that if ##\mathscr{U}## is an open cover of ##X## such that the restriction ##\mathscr{F}|_U## is flasque for every ##U\in \mathscr{U}##, then ##\mathscr{F}## is flasque.
Note: A sheaf ##\mathscr{G}## on ##X## is flasque if for all open subsets ##U\subset X##, the restriction map ##\mathscr{G}(X) \to \mathscr{G}(U)## is surjective.
Note: A sheaf ##\mathscr{G}## on ##X## is flasque if for all open subsets ##U\subset X##, the restriction map ##\mathscr{G}(X) \to \mathscr{G}(U)## is surjective.