Partial Metric Topology

Metric spaces are inevitably Hausdorff and so cannot, for example, be used to study non‐Hausdorff topologies such as those required in the Tarskian approach to programming language semantics. This paper presents a symmetric generalised metric for such topologies, an approach which sheds new light on how metric tools such as Banach's Theorem can be extended to non‐Hausdorff topologies.