In mathematics, particularly in the field of topology and differential geometry, a "germ" is a concept used to study the local behavior of functions or spaces at a point. Specifically, a germ refers to an equivalence class of functions or objects that are defined in a neighborhood of a point, where two functions are considered equivalent if they agree on some neighborhood of that point.
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A germ at a point is an equivalence class of functions defined on a neighbourhood of the point: two representatives are equivalent if they agree on some smaller neighbourhood. A germ of a holomorphic function requires its representatives to be holomorphic functions; smooth and continuous germs use their corresponding classes of functions. The germ retains local behavior while forgetting the representative's values farther from the point.