On the lightness of the limit of sequence of mappings satisfying some modular inequality

TL;DR

This paper proves that the locally uniform limit of a sequence of certain space mappings satisfying a modular inequality is light, generalizing known results about mappings with bounded distortion.

Contribution

It introduces a broader class of mappings and shows their limits are light, extending classical theorems on openness and discreteness.

Findings

Limit mappings are light under given conditions

Generalizes classical theorems on bounded distortion mappings

Extends understanding of modular inequalities in mapping theory

Abstract

A paper is devoted to study of one class of space mappings which are more general than mappings with bounded distortion. It is showed that a locally uniformly limit of a sequence of mappings $f:D\rightarrow {\Bbb R}^n$ of domain $D\subset{\Bbb R}^n,$ $n\geqslant 2,$ satisfying one inequality with respect to $p$-modulus of families of curves, is light. The above statement is a generalization of well-known theorem about openness and discreteness of uniformly limit of a sequence of mappings with bounded distortion.