On the openness and discreteness of mappings with unbounded characteristic of quasiconformality

Abstract

The paper is devoted to the investigation of topological properties of space mappings. It is shown that orientation-preserving mappings $ f:D \to \overline {{\mathbb{R}^n}} $ in a domain $ D \subset {\mathbb{R}^n} $ , n ≥ 2; which are more general than mappings with bounded distortion, are open and discrete if a function Q corresponding to the control of the distortion of families of curves under these mappings has slow growth in the domain f (D), e.g., if Q has finite mean oscillation at an arbitrary point y 0 ∈ f (D).