On removable singularities of mappings in uniform spaces

E. A. Sevostyanov1, S. A. Skvortsov2, N. S. Ilkevych3
1) Zhytomyr Ivan Franko State University Zhytomyr, Ukraine Institute of Applied Mathematics and Mechanics of NAS of Ukraine, Slovyansk, Ukraine; 2, 3) Zhytomyr Ivan Franko State University Zhytomyr, Ukraine
The paper is devoted to the study of mappings of two metric spaces that distort the modulus of families of paths by analogy with the Poletskii inequality.We deal with the situation when the mapping acts in a space that admits weak sphericalization, while the corresponding extended metric space is uniform. For such mappings, the possibility of continuous extension to an isolated boundary point is proved and, as a consequence, an analogue of the Sokhotski-Casorati-Weierstrass theorem is obtained.
metric spaces; quasiconformal mappings; mappings with bounded and finite distortion; singularities; moduli of families of paths
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Matematychni Studii
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