Asymmetric Completions of Partial Metric Spaces - Imamura, Takuma (Topology Proceedings, 2020)
Xun Ge and Shou Lin (2015) prove the existence and the uniqueness of p-Cauchy completions of partial metric spaces under symmetric denseness. They ask if every (non-empty) partial metric space X has a p-Cauchy completion X such that X is dense but not symmetrically dense in X. We construct asymmetric p-Cauchy completions for all non-empty partial metric spaces. This gives a positive answer to the question. We also provide a nonstandard construction of partial metric completions.