  Let $\Omega\subset\mathbb{R}^n$ be an open set and let $f\in
W^{1,p}(\Omega,\mathbb{R}^n)$ be a weak (sequential) limit of Sobolev
homeomorphisms. Then $f$ is injective almost everywhere for $p>n-1$ both in the
image and in the domain. For $p\leq n-1$ we construct a strong limit of
homeomorphisms such that the preimage of a point is a continuum for every point
in a set of positive measure in the image and a topological image of a point is
a continuum for every point in a set of positive measure in the domain.
