• Interaction With Unions I. The diagram

    commutes, i.e. we have

    \[ \bigcap _{W\in \mathcal{U}\cup \mathcal{V}}W=\webleft(\bigcap _{U\in \mathcal{U}}U\webright)\cap \webleft(\bigcap _{V\in \mathcal{V}}V\webright) \]

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


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