The Half Disc Topology is partially metrizable - Assaf, Samer; Cuchta, Tom (Topology Proceedings, 2022)
In this paper we answer the long standing conjecture: "Is a Hausdorff partial metric space metrizable?", albeit in a negative way. To accomplish this, we show how to partially metrize the Half Disc Topological Space, a non-metrizable Completely Hausdorff space. We end by suggesting a new conjecture to replace the one we disproved.