On Sokhotski--Casorati--Weierstrass theorem on metric spaces

TL;DR

This paper investigates the boundary behavior of generalized quasiconformal mappings in metric spaces, establishing conditions for their continuous extension and deriving an analog of the Sokhotski--Weierstrass theorem.

Contribution

It introduces an analog of the Sokhotski--Weierstrass theorem for generalized quasiconformal mappings in metric spaces under specific conditions.

Findings

Mappings have continuous extensions under certain conditions

An analog of Sokhotski--Weierstrass theorem is proved

Boundary behavior of mappings is characterized

Abstract

In a neighborhood of isolated point of a domain of a metric space, a behavior of generalized quasiconformal mappings is studied. It is proved that, mappings mentioned above have continuous extension to the domain at some additional conditions. As consequence, an analog of Sokhotski--Weierstrass theorem is obtained.