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

Abstract

The paper is devoted to the investigation of the topological properties of space mappings. It is shown that sense-preserving mappings $f : D \rightarrow \overline{\mathbb{R}^n}$ 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 $y0 \in f(D)$.