Image and inverse image may also be defined for general binary relations, not just functions.

The exceptional inverse image is in general defined on the level of derived categories only.

To do this requires two steps: First compute an inverse image of each point to be visited; then sort the values.

Morphisms: all functions such that the inverse image of every closed set is closed.

The easy way to remember the definitions above is to notice that finding an inverse image is used in both.

This is because inverse image preserves union and intersection.

Thus the inverse image would be a 1-manifold with boundary.

That is, in each step, we choose at random one of the inverse images of .

The inverse image of any noncritical value of a holomorphic map.

Also, the two inverse images of under the doubling map ( and ) are both in every critical arc.