The probabilistic powerdomain from a topological viewpoint

We prove that the probabilistic powerdomain of a coherent locally finitary compact T0 space is coherent quasicontinuous. As a result, we obtain a novel proof of Larrecq's and Jung's result in 2014. The main tool for our proof is the weak topology on the probabilistic powerdomain. In addition, we show that a dcpo L is continuous (resp., quasicontinuous, coherent quasicontinuous, meet-continuous) if the probabilistic powerdomain V(L) over L is continuous (resp., quasicontinuous, Lawson compact quasicontinuous, meet-continuous), which confirms a conjecture of Jones in her doctoral thesis.