On the Boundary Behavior of One Class of Mappings in Metric Spaces - Afanas'eva, E. S. (Ukrains’kyi Matematychnyi Zhurnal, 2014)
We study the problem of extension to the boundary of continually ring Q-homeomorphisms relative to a p-module between continual domains in metric spaces with measures and formulate the conditions for the function Q and the boundaries of domains under which every continually ring Q-homeomorphism admits a continuous or homeomorphic extension to the boundary. The accumulated results yield, in particular, important applications to fractals in ℝ n , n ≥ 2.