TY - JOUR
AU - E. A. Sevost'yanov
PY - 2009/01/25
Y2 - 2023/03/28
TI - Removal of singularities and analogs of the Sokhotskii–Weierstrass theorem for Q-mappings
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 61
IS - 1
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3007
AB - 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.
ER -