• Relation to Direct Images. We have
    \begin{align*} f_{!}\webleft (U\webright ) & = f_{*}\webleft (U^{\textsf{c}}\webright )^{\textsf{c}}\\ & = Y\setminus f_{*}\webleft (X\setminus U\webright ) \end{align*}

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


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