• Relation to Direct Images With Compact Support. We have
    \begin{align*} f_{*}\webleft (U\webright ) & = f_{!}\webleft (U^{\textsf{c}}\webright )^{\textsf{c}}\\ & \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}Y\setminus f_{!}\webleft (X\setminus U\webright )\end{align*}

    for each $U\in \mathcal{P}\webleft (X\webright )$.


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