Finite $C^0$-determinacy of real analytic map germs with isolated instability

Abstract

Let f : (Rn; 0) (Rp; 0) be a real analytic map germ with isolated instability. We prove that if n = 2 and p = 2; 3, then f is finitely C0-determined. This result can be seen as a weaker real counterpart of Mather-Gaffney finite determinacy criterion.