Item 16 (005P) — The Clowder Project

Preferences





Font:

PDF Style:

Here's a breakdown of the differences between each PDF style:

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.

Bijectivity. Given $U,V\in \mathcal{P}\webleft (X\webright )$, the maps
\begin{align*} U\mathbin {\triangle }- & \colon \mathcal{P}\webleft (X\webright ) \to \mathcal{P}\webleft (X\webright ),\\ -\mathbin {\triangle }V & \colon \mathcal{P}\webleft (X\webright ) \to \mathcal{P}\webleft (X\webright ) \end{align*}

are bijections with inverses given by

\begin{align*} \webleft (U\mathbin {\triangle }-\webright )^{-1} & = -\cup \webleft (U\cap -\webright ),\\ \webleft (-\mathbin {\triangle }V\webright )^{-1} & = -\cup \webleft (V\cap -\webright ). \end{align*}

Moreover, the map
is a bijection of $\mathcal{P}\webleft (X\webright )$ onto itself sending $U$ to $V$ and $V$ to $U$.

Noticed something off, or have any comments? Feel free to reach out!

You can also use the contact form below: