Item 1 (008N) — 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`

The image part of the direct image with compact support $f_{!}\webleft (U\webright )$ of $U$ is the set $f_{!,\text{im}}\webleft (U\webright )$ defined by
\begin{align*} f_{!,\text{im}}\webleft (U\webright ) & \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}f_{!}\webleft (U\webright )\cap \mathrm{Im}\webleft (f\webright )\\ & = \webleft\{ b\in B\ \middle |\ \text{we have $f^{-1}\webleft (b\webright )\subset U$ and $f^{-1}\webleft (b\webright )\neq \emptyset $}\webright\} .\end{align*}

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