If we have a homeomorphism h: R^n \to R^n from n-dimensional euclidean space to itself, is there any way of telling if h is smooth or not ?? Or is there any way to show (at least) if h is a C^1 function or not ?? are there any papers about this matter ?
In particullar, it would ne nice if there is some way of telling if h is smooth (or just C^1) by using convergence of sequences in R^n.