"Understanding Machine Learning: From Theory to Algorithms" the universal approximation theorem
Yes, it is applicable to a Boolean function and you can modify the result to compact set. 

A result where the codomian is $[-1, 1]$ would cover regression and not restricting ourself to boolean. 

You might or might not have a result for $f: \mathbb{R}^n \to \mathbb{R}$. A theorem states what conditions it requires in order to hold, for conditions that are not promised by a theorem, you have to check carefully whether the same conclusion can still apply. In particular, if the proof uses compactness, then you can't replace $[-1,1]$ with $\mathbb{R}$.