ITES2001 Fourth Italian-Spanish conference on General Topology and its applications Bressanone, 27-30 June 2001

Completion of partial metrics

S. Oltra, S. Romaguera, E. A. Sánchez-Pérez Departamento de Matemática Aplicada Universidad Politécnica de Valencia, Spain

We show that the bicompletion of a weightable quasi-metric space is a weightable quasi-metric space. From this result we deduce, among other facts, that any partial metric space has an (up to isometry) unique partial metric bicompletion. Some consequences are derived.