• Interaction With Surjections. If $f$ is surjective, then we have
    \begin{align*} f_{!,\text{im}}\webleft (U\webright ) & \subset f_{*}\webleft (U\webright ),\\ f_{!,\text{cp}}\webleft (U\webright ) & = \text{Ø},\\ f_{!}\webleft (U\webright ) & \subset f_{*}\webleft (U\webright ) \end{align*}

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


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