direct image

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

$(f_{*}ℱ)(V)=ℱ(f^{-1}(V))$

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