# 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

*x*_{0} 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

*x*_{0} such that for all

*x* ε

*U*, the identity

*f*(

*x*) =

*g*(

*x*) holds. All

*local* properties of

*f* at

*x*_{0} depend only on which germ

*f* belongs to.