New Topologies on Partial Metric Spaces and M-Metric Spaces

In this paper, we present new definitions for partial metric space(PMS) and M-metric space(MMS). We obtain some of its properties by presenting the topology of those spaces. The new topology is weaker than the previously defined topology for PMS and MMS. We remove the condition \(p(x, x) \le p(x, y)\) from partial metric space and \(m_{x,y} \le m(x, y)\) from M-metric space, as well. By our definitions, the new topology is Hausdorff, while the first topology isn’t.