Embedding Cantor set into a Surface

Question

I'm looking for a result that generalized the following theorem to closed surface.

Theorem: (All Cantor set in the plane are tame) Suppose $C$ is a Cantor set and $f:C \to \mathbb{R}^2$ is an embedding of $C$ in the plane. Then the map $f$ extends to a homeomorphism $F:\mathbb{R}^2 \to \mathbb{R}^2$.

Is there any result that genereralize this theorem to closed surfaces instead of $\mathbb{R}^2$?