• Associativity. The diagram

    commutes, i.e. we have

    \[ \bigcup _{U\in {\scriptsize \displaystyle \bigcup _{A\in \mathcal{A}}A}}U=\bigcup _{A\in \mathcal{A}}\webleft (\bigcup _{U\in A}U\webright ) \]

    for each $\mathcal{A}\in \mathcal{P}\webleft (\mathcal{P}\webleft (\mathcal{P}\webleft (X\webright )\webright )\webright )$.


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