Let's open R.O.Wells "Differential Analysis on Complex Manifolds" p. 53 and have a look at the Proposition 3.5 stating that all fine sheaves are soft (over a paracompact Hausdorff $X$). In the proof we consider the covering of a closed $S \subset X$ by open $U_i$. Why can't we just take a single $U_1$ covering $S$? A section $s$ over $S$ by definition is an element of a direct limit, so it should have a representative in some neighborhood of $S$ and we could just set $U_1$ to be that neighborhood. Or couldn't we? But the proof is more complicated than that and I'm confused...
