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

Gunther Jäger, T. M. G. Ahsanullah

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

Subject classification

54A20; 54A40; 54E35; 54E70; 54E99.

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