On lightness of one class of mappings in metric spaces

TL;DR

This paper proves that certain metric space mappings with specific inequalities and finite mean oscillation conditions have light preimages, contributing to the understanding of their geometric properties.

Contribution

It introduces conditions under which mappings in metric spaces are light, linking modulus inequalities and finite mean oscillation to geometric lightness.

Findings

Mappings satisfying the inequality are light when associated distortion functions have finite mean oscillation.

Preimages under these mappings are proven to be light.

The results extend understanding of geometric properties of mappings in metric spaces.

Abstract

For mappings in metric spaces satisfying one inequality with respect to modulus of families of curves, there is proved a lightness of preimage under the mapping. It is proved that, the mappings, satisfying estimate mentioned above, are light, whenever a function which corresponds to distortion of families of curves under the mapping, is of finite mean oscillation at every point.