If the <germ of a sheaf section> $s_p$ is zero, then by the definition of a <stalk of a sheaf> there is a neighbourhood $V$ of $p$ on which $s|_V=0$. Every point of $V$ also has zero germ. Thus the complement of $\operatorname{Supp}s$ is open, so the <support of a sheaf section> is closed.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 113 / 4 / a / Solution

 Solution (source code)