• Interaction With Intersections of Families of Subsets I. The diagram

    does not commute in general, i.e. we may have

    \[ \bigcap _{W\in \webleft [\mathcal{U},\mathcal{V}\webright ]_{\mathcal{P}\webleft (X\webright )}}W\neq \webleft[\bigcap _{U\in \mathcal{U}}U,\bigcap _{V\in \mathcal{V}}V\webright]_{X} \]

    in general, where $\mathcal{U}\in \mathcal{P}\webleft (\mathcal{P}\webleft (X\webright )\webright )$.


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