I'm studying sheaf cohomology, and I've seen that Čech and derived functor cohomologies agree, at least on paracompact Hausdorff topological spaces.
Is there a simple example of a topological space $X$ with a sheaf $\mathcal F$ such that these two cohomologies don't agree? (I don't have any knowledge of schemes, I want $X$ to be a topological space)