Skyscraper sheaf cohomology
= Skyscraper sheaf cohomology
{title2=$H^0(X,i_*A)=A,\quad H^{i>0}(X,i_*A)=0$}
For any point inclusion $i:\{x\}\hookrightarrow X$, the <skyscraper sheaf> $i_*A$ has restriction maps that are identities or maps to zero. It is <flasque>, so its higher <sheaf cohomology> vanishes and its <global sections> are $A$. This requires no assumption that $x$ is closed.