On equicontinuity of homeomorphisms in a closure of a domain in metric spaces

TL;DR

This paper investigates conditions under which families of homeomorphisms, generalizing quasiconformal mappings in metric spaces, are equicontinuous on the closure of a domain, contributing to the understanding of their boundary behavior.

Contribution

It establishes new conditions on metric spaces and domain boundaries that ensure equicontinuity of these generalized homeomorphisms.

Findings

Families of homeomorphisms are equicontinuous under certain boundary conditions.

Generalization of quasiconformal mappings in metric spaces.

Provides criteria for boundary behavior of homeomorphisms.

Abstract

In the present paper, homeomorphisms in metric spaces which generalize quasiconformal mappings, are investigated. It is proved that, at some conditions on metric spaces and boundaries of corresponding domains, families of above mappings are equicontinuous in a closure of a given domain.