• Interaction With Inverse Images. Let $f\colon X\to Y$ be a function. The diagram

    commutes, i.e. we have an equality of sets

    \[ f^{-1}\webleft (\webleft [U,V\webright ]_{Y}\webright )=\webleft [f^{-1}\webleft (U\webright ),f^{-1}\webleft (V\webright )\webright ]_{X}, \]

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


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