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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.