Definition:Image Filter

Definition
Let $$X, Y$$ be sets, $$f: X \to Y$$ a mapping and $$\mathcal F \subset \mathcal P \left({X}\right)$$ a filter on $$X$$.

Then
 * $$f(\mathcal F) := \left\{{U \subseteq Y: f^{-1} \left({U}\right) \in \mathcal F}\right\}$$

is a filter on $$Y$$, called the image filter of $$\mathcal F$$ with respect to $$f$$.

Also see

 * Image of a Subset