Skvortsov S. A.
Ukr. Mat. Zh. - 2019. - 71, № 7. - pp. 938-951
We study the problem of local behavior of maps in the closure of a domain in the Euclidean space. The equicontinuity of families of these mappings is established in the case where the mapped domain is not fixed. We separately consider the domains with bad and good boundaries, as well as the homeomorphisms and maps with branching.
Ukr. Mat. Zh. - 2018. - 70, № 7. - pp. 952-687
For mappings in metric spaces satisfying one inequality with respect to the modulus of families of curves, we establish the property of lightness of the limit mapping. It is shown that the uniform limit of these mappings is a light mapping, whenever the function responsible for the distortion of the families of curves, is of finite mean oscillation at every point. In addition, for one class of homeomorphisms of metric spaces, we prove theorems on the equicontinuity of the families of inverse mappings.