ON QUASI-METRIC AND METRIC SPACES

Given a space X with a quasi-metric rho it is known that the so-called p-chain approach can be used to produce a metric in X equivalent to rho(p) for some 0 < p <= 1, hence also a quasi-metric <(rho)over tilde> equivalent to rho with better properties. We refine this result and obtain an exponent p which is, in general, optimal.