# Definition:Image Filter

## Definition

Let $S_1, S_2$ be sets.

Let $\powerset {S_1}$ and $\powerset {S_2}$ be the power sets of $S_1$ and $S_2$ respectively.

Let $f: S_1 \to S_2$ a mapping.

Let $\FF \subset \powerset {S_1}$ be a filter on $S_1$.

Then $f \sqbrk \FF := \set {U \subseteq S_2: f^{-1} \sqbrk U \in \FF}$ is the image filter of $\FF$ (on $S_2$) with respect to $f$.