Characterization of quantale-valued metric spaces and quantale-valued partial metric spaces by convergence

Abstract

We identify two categories of quantale-valued convergence tower spaces that are isomorphic to the categories of quantale-valued metric spaces and quantale-valued partial metric spaces, respectively. As an application we state a quantale-valued metrization theorem for quantale-valued convergence tower groups.

Keywords

• L-metric space
• L-partial metric space
• L-convergence tower space
• L-convergence tower group
• metrization