Relation With Sheaves
The idea of germ is behind the definition of sheaves and presheaves. A presheaf on a topological space X is an assignment of an Abelian group to each open set U in X. Typical examples of Abelian groups here are: real valued functions on U, differential forms on U, vector fields on U, holomorphic functions on U (when X is a complex space), constant functions on U and differential operators on U.
If then there is a restriction map, satisfying certain compatibility conditions. For a fixed x, one says that elements and are equivalent at x if there is a neighbourhood of x with resWU(f) = resWV(g) (both elements of ). The equivalence classes form the stalk at x of the presheaf . This equivalence relation is an abstraction of the germ equivalence described above.
Read more about this topic: Germ (mathematics)
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