Item 6 (01GG) — The Clowder Project

Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
Style 4	`book`	Computer Modern	`amsthm`

Interaction With Unions II. The diagram
commute, i.e. we have
\begin{align*} U\cup \webleft(\bigcap _{V\in \mathcal{V}}V\webright) & = \bigcap _{V\in \mathcal{V}}\webleft (U\cup V\webright ),\\ \webleft(\bigcap _{U\in \mathcal{U}}U\webright)\cup V & = \bigcap _{U\in \mathcal{U}}\webleft (U\cup V\webright )\end{align*}

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

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