On convergence and compactness of space homeomorphisms

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 ${\Bbb R}^n$fixingtwopointsiscompactprovidedthatthefunction$Q$ is of finite mean oscillation. These results will have wide applications to Sobolev’s mappings.