Germ (mathematics)

In mathematics,germ an equivalence classcontinuous functions from one topological spaceanother (often from real lineitself),which one point x₀ indomain has been singled out as privileged, where two functions fgequivalent precisely if theresome open neighborhood Ux₀ such thatall x ε U,identity f(x) = g(x) holds. All local propertiesf at x₀ depend only on which germ f belongs to.