Item 8 (01KN) — The Clowder Project

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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`

*To be replaced with Linus Romer's Elemaints when it is released.

Interaction With Unions of Families of Subsets II. The diagram

commutes, i.e. we have

\[ \webleft[\bigcup _{U\in \mathcal{U}}U,V\webright]_{X}= \bigcap _{U\in \mathcal{U}}\webleft [U,V\webright ]_{X} \]

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

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