On the sets of branch points of mappings more general than quasiregular

It is shown that if a point x ₀ ∊ ℝⁿ, n ≥ 3, is an essential isolated singularity of an open discrete Q-mapping f : D → $\overline {\mathbb {R}^n}$, B _f is the set of branch points of f in D; and a point z ₀ ∊ $\overline {\mathbb {R}^n}$ is an asymptotic limit of f at the point x ₀; then, for any neighborhood U containing the point x ₀; the point z ₀ ∊ $\overline {f\left( {B_f \cap U} \right)}$ provided that the function Q has either a finite mean oscillation at the point x ₀ or a logarithmic singularity whose order does not exceed n − 1: Moreover, for n ≥ 2; under the indicated conditions imposed on the function Q; every point of the set $\overline {\mathbb {R}^n}$\ f(D) is an asymptotic limit of f at the point x ₀. For n ≥ 3, the following relation is true: $\overline {\mathbb{R}^n } \backslash f\left( D \right) \subset \overline {f\,B_f }$ . In addition, if $\infty \notin f\left( D \right)$, then the set f B _f is infinite and $x_0 \in \overline {B_f }$.