Inverse Image Definition Math. Let f be a presheaf over a topological space y. X y is a continuous map then we have a natural presheaf on x given by.
F 1 y f 1 y y y. Preimage point a point to which a transformation has been applied. Inverse image of a set.
Remark 2 2 the above definition does not require that f be injective or have an inverse.
The preimage of a member of the field of is the set used in the definition of well founded below the preimage or inverse image of a set b y under f is the subset of x defined by f 1 b x in x. Let f be a presheaf over a topological space y. Most people will say that the inverse image is the sheafification of that but it ll be enough to consider this for now. More generally evaluating a given function f at each element of a given subset a of its domain produces a set called the image of a under or through f similarly the inverse image or preimage of a given subset b of the codomain of f is the set of all elements of the domain that map to the members.