direct image

If $f:X\to Y$ is a continuous map of topological spaces and $\mathcal{F}$ is a sheaf on $X$ , the direct image sheaf, $f_{*}\mathcal{F}$ on $Y$ is defined by

$(f_{*}\mathcal{F})(V)=\mathcal{F}(f^{-1}(V))$

for open sets $V\subset Y$ , with the restriction maps induced from those of $\mathcal{F}$ .