Local behavior of mappings of metric spaces with branching

The local behavior of mappings with the inverse Poletsky inequality between metric spaces is studied. case where one satisfies condition weak sphericalization, similar to Riemannian sphere (extended Euclidean space), and locally linearly connected under a mapping considered. It proved that equicontinuity corresponding families two domains, which domain weakly flat boundary, another fixed compact closure, weight in main being supposed be integrable.