Family of Computably Enumerable Sets

Please help prove the following statement:

There exists an single-valued computable enumeration of a family of computably enumerable sets.


1) Let $ S$ be nonempty countable set (possibly finite). Any surjective map $ \nu\colon \omega \twoheadrightarrow S$ from the set $ \omega$ of natural numbers onto the set $ S$ is called an enumeration.

2) An enumeration $ \nu$ is single-valued if $ \nu$ is a bijective, i.e. $ \nu$ (x) /= $ \nu$ (y) for any x /= y