On the Existence of Bi-Lipschitz Equivalent Metrics in Semimetric Spaces.

We provide an overview of the known problem on the existence of a bi-Lipschitz equivalent metric with respect to a given quasi-ultrametric, revisiting known results and counterexamples in an unified approach based on the existence of a relaxed polygonal inequality. We present new proofs and characterizations of classical results using different techniques. [ABSTRACT FROM AUTHOR]