On the openness and discreteness of mappings with unbounded characteristic of quasiconformality - Sevost'yanov, E. A. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
The paper is devoted to the investigation of the topological properties of space mappings. It is shown that sense-preserving mappings $f : D → \overline{\mathbb{R}^n}$ in a domain $D \subset \mathbb{R}^n$, n ≥ 2, which are more general thanmappings with bounded distortion, are open and discrete if a function Q corresponding to the control of thedistortion of families of curves under these mappings has slow growth in the domain f(D), e.g., if Q hasfinite mean oscillation at an arbitrary point $y0 \in f(D)$.