• Oplax Preservation of Limits. We have an inclusion of sets
    \[ R^{-1}\webleft (\bigcap _{i\in I}U_{i}\webright )\subset \bigcap _{i\in I}R^{-1}\webleft (U_{i}\webright ), \]

    natural in $\webleft\{ U_{i}\webright\} _{i\in I}\in \mathcal{P}\webleft (B\webright )^{\times I}$. In particular, we have inclusions

    \[ \begin{gathered} R^{-1}\webleft (U\cap V\webright ) \subset R^{-1}\webleft (U\webright )\cap R^{-1}\webleft (V\webright ),\\ R^{-1}\webleft (A\webright ) \subset B, \end{gathered} \]

    natural in $U,V\in \mathcal{P}\webleft (B\webright )$.


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