Infinity valued partial metrics

A partial metric is a generalised metric incorporating non-zero self-distance. It was introduced by Matthews in Computer Science, and connected well with Kopperman's long standing interest in generalised metrics and non-Hausdorff topology. In this article we further generalise partial metrics by incoporating ∞ as a distance. We prove that a so-called infinite partial metric induces a partial metrizable topology, but not in general vice verse.