Germ (mathematics)

From Academic Kids

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 xU, 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

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