On quasi-metric and metric spaces

Abstract

Given a space X X with a quasi-metric ρ \rho it is known that the so-called p p -chain approach can be used to produce a metric in X X equivalent to ρ p \rho ^p for some 0 > p ≤ 1 0>p\le 1 , hence also a quasi-metric ρ ~ \tilde {\rho } equivalent to ρ \rho with better properties. We refine this result and obtain an exponent p p which is, in general, optimal.