On the Boundary Behavior of One Class of Mappings in Metric Spaces
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.
English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 1, pp 16-29.
Citation Example: Afanas'eva E. S. On the Boundary Behavior of One Class of Mappings in Metric Spaces // Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 17–29.