Cutting description of trivial 1-cohomology

TL;DR

This paper characterizes when the first cohomology group is trivial for a wide class of metric spaces, linking cohomology to the connectedness of open sets.

Contribution

It introduces a new characterization that connects trivial 1-cohomology with the connectedness properties of open sets in metric spaces.

Findings

Provides a criterion for trivial 1-cohomology in metric spaces

Links cohomology triviality to open set connectedness

Broad applicability to various metric space classes

Abstract

A characterisation of trivial 1-cohomology for a broad class of metric spaces is presented. The condition ties cohomology and connectedness properties of open sets.