On Sokhotski–Casorati–Weierstrass theorem on metric spaces

Abstract

ABSTRACTThe paper is devoted to maps on metric spaces whose quasiconformal characteristic satisfies certain restrictions of integral type. First of all, we prove that the so-called ring Q-mappings have a continuous extension to an isolated boundary point if the function has a finite mean oscillation at the point. As a corollary of this observation, we obtain the corresponding analog of the well-known Sokhotski–Casorati–Weierstrass theorem for ring Q-mappings.