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

    commutes, i.e. we have

    \[ f^{-1}\webleft (U\cap V\webright )=f^{-1}\webleft (U\webright )\cap f^{-1}\webleft (V\webright ) \]

    for each $U,V\in \mathcal{P}\webleft (Y\webright )$.


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