Let $f\colon(\mathbb R^n,0)\to(\mathbb R^p,0)$ be a real analytic map germ with isolated instability. We prove that if $n=2$ and $p=2,3$, then $f$ is finitely $C^0$-determined. This result can be seen as a weaker real counterpart of Mather-Gaffney finite determinacy criterion.
"Finite $C^0$-determinacy of real analytic map germs with isolated instability." Publ. Mat. 64 (2) 563 - 575, 2020. https://doi.org/10.5565/PUBLMAT6422008