# Removal of singularities and analogs of the Sokhotskii–Weierstrass theorem for Q-mappings

### Abstract

We prove that an open discrete*Q*-mapping \( f:D \to \overline {{\mathbb{R}^n}} \) has a continuous extension to an isolated boundary point if the function

*Q*(

*x*) has finite mean oscillation or logarithmic singularities of order at most

*n*– 1 at this point. Moreover, the extended mapping is open and discrete and is a

*Q*-mapping. As a corollary, we obtain an analog of the well-known Sokhotskii–Weierstrass theorem on

*Q*-mappings. In particular, we prove that an open discrete

*Q*-mapping takes any value infinitely many times in the neighborhood of an essential singularity, except, possibly, for a certain set of capacity zero.

Published

25.01.2009

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 61, no. 1, Jan. 2009, pp. 116-2, https://umj.imath.kiev.ua/index.php/umj/article/view/3007.

Issue

Section

Research articles