This article is about the mathematical notion of an equivalence class of functions. For the disease-causing organisms see Germ. For the Pre-Raphaelite journal entitled The Germ, see The Germ (periodical).

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. Two functions f and g are equivalent precisely if there is some open neighborhood U of x₀ such that for all x ∈ U, the identity f(x) = g(x) holds. All local properties of f at x₀ depend only on which germ f belongs to.

When the spaces are Riemann surfaces, germs can be viewed as power series, and thus the set of germs can be considered to be the analytic continuation of an analytic function. The article on Riemann surfaces provides additional detail on germs in this context.

See also: Sheaf