On the openness and discreteness of the mappings satisfying one inequality with respect to $p$-modulus

TL;DR

This paper investigates the topological properties of certain space mappings that satisfy a specific modulus inequality related to the $p$-modulus, demonstrating conditions under which these mappings are open and discrete.

Contribution

It establishes conditions on the function $Q$ that ensure sense-preserving mappings satisfying a $p$-modulus inequality are open and discrete.

Findings

Mappings are open and discrete under certain conditions on $Q$.

The study extends understanding of topological behavior of mappings constrained by modulus inequalities.

Provides criteria for the openness and discreteness of mappings in terms of $Q$.

Abstract

A paper is devoted to study of topological properties of some class of space mappings. It is showed that, sense preserving mappings $f:D\rightarrow \overline{{\Bbb R}^n}$ of a domain $D\subset{\Bbb R}^n,$ $n\geqslant 2,$ satisfying some modulus inequality with respect to $p$-modulus of families of curves, are open and discrete at some restrictions on a function $Q,$ which determinate inequality mentioned above.