Item 18 (005T) — 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 Powersets and Vector Spaces I. The pair $\webleft (\mathcal{P}\webleft (X\webright ),\alpha _{\mathcal{P}\webleft (X\webright )}\webright )$ consisting of
- The group $\mathcal{P}\webleft (X\webright )$ of Item 17;
- The map $\alpha _{\mathcal{P}\webleft (X\webright )}\colon \mathbb {F}_{2}\times \mathcal{P}\webleft (X\webright )\to \mathcal{P}\webleft (X\webright )$ defined by
  \begin{align*} 0\cdot U & \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\text{Ø},\\ 1\cdot U & \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}U; \end{align*}
is an $\mathbb {F}_{2}$-vector space.

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