DS-partial metric spaces and domain theory

In this paper, we establish some connections between partial metric spaces and domain theory, and give a characterization of stable partially metrizable dspaces. First, the concept of S -partial metrics on posets is introduced. Then it is demonstrated that the open ball topology is coarser than the Scott topology in an S -partial metric space, and that the partially metrizable d -space is exactly the DS -partial metric space. In addition, some conditions are provided to ensure that the open -ball topology and the Scott topology coincide in an S -partial metric space. Moreover, we prove that, for an S -partial metric space (X, <=, p), (X, Op(X)) is sober iff the set of all limit points of every self -convergent sequence is directed. Finally, we propose the notion of DS -valuation space and obtain the result that there is a bijection between stable DS -partial metric spaces and DS -valuation spaces, thereby giving the characterization of stable partially metrizable d -spaces. (c) 2024 Elsevier B.V. All rights reserved.