Germ (mathematics)

In mathematics, a germ is an equivalence class of continuous functions from one topological space to another (often from the real line to itself), in which one point x₀ in the domain has been singled out as privileged, where two functions f and g are equivalent precisely if there is some open neighborhood U of x₀ such that for all x ε U, the identity f(x) = g(x) holds. All local properties of f at x₀ depend only on which germ f belongs to.