Here we define the mathematical concept of a map germ. Given the set of all maps from one manifold to another we can collect maps together under an equivalence relation. These equivalence classes are called map germs.
Consider two manifolds and Let and be open neighbourhoods of the point Let and We may induce an equivalence relation on the space of mappings as follows: we say that if there exists an open such that i.e. the restriction of to coincides with the restriction of to