On convergence and compactness of space homeomorphisms

Abstract

Various theorems on convergence of general space homeomorphisms are proved and, on this basis, theorems on convergence and compactness for classes of the so-called ring $Q$--homeomorphisms are obtained. In particular, it was established by us that a family of all ring $Q$--homeomorphisms $f$ in ${\Bbb R}^n$ fixing two points is compact provided that the function $Q$ is of finite mean oscillation. These results will have wide applications to Sobolev's mappings.