About some mappings in $\lambda(r)$-regular metric spaces

TL;DR

This paper investigates conditions under which certain mappings in metric spaces with measures can be extended continuously or homeomorphically to the boundary, focusing on $Q$-homeomorphisms in $ ext{lambda}(r)$-regular spaces.

Contribution

It introduces new boundary extension criteria for $Q$-homeomorphisms in $ ext{lambda}(r)$-regular metric spaces with measures, expanding understanding of boundary behavior.

Findings

Established boundary extension conditions for $Q$-homeomorphisms.

Identified specific properties of functions $Q(x)$ and domain boundaries.

Provided theoretical framework for boundary extension in measure metric spaces.

Abstract

It is formulated conditions on functions $Q(x)$ and boundaries of domains under which every $Q$-homeomorphism admits continuous or homeomorphic extension to the boundary in metric spaces with measures.