A germ is an equivalence class of objects defined near a specified point, where two representatives are equivalent when they agree
on some smaller neighborhood. For functions at the origin, the representatives can
be functions on different neighborhoods, and equality of germs means equality after
restriction. Holomorphic function germs on
form the ring 
of convergent power
series. Subset germs are defined by agreement on a neighborhood in the same way.
A homeomorphism germ of pairs 
and 
is represented by a homeomorphism
between neighborhoods fixing the origin and taking one zero
set onto the other. It preserves the embedded topological germ, but need not
preserve the analytic structure or the defining function.
