On boundary behavior of typical mappings

In this article the structure of radial limit sets is investigated for typical mappings defined in the unit ball in $n$-dimensional Euclidean space $\mathbb R^n$ for $n\ge2$ and belonging to various function spaces. The structure of the sets of all such mappings in these function spaces is also studied. As an auxiliary result we obtain a description of the structure of typical compact sets in $\mathbb R^n$ for $n\ge1$.