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

  • E. A. Sevost'yanov


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.
How to Cite
Sevost’yanov, E. A. “Removal of Singularities and Analogs of the Sokhotskii–Weierstrass Theorem for Q-Mappings”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, no. 1, Jan. 2009, pp. 116-2,
Research articles