Item 17 (0091) — 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 Injections. If $f$ is injective, then we have
\begin{gather*} f_{!,\text{im}}\webleft (U\webright ) = f_{*}\webleft (U\webright ),\\ f_{!,\text{cp}}\webleft (U\webright ) = Y\setminus \mathrm{Im}\webleft (f\webright ),\\ \begin{aligned} f_{!}\webleft (U\webright ) & = f_{!,\text{im}}\webleft (U\webright )\cup f_{!,\text{cp}}\webleft (U\webright )\\ & = f_{*}\webleft (U\webright )\cup \webleft (Y\setminus \mathrm{Im}\webleft (f\webright )\webright ) \end{aligned}\end{gather*}

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

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