Ge and Lin (2015) proved the existence and the uniqueness of p-Cauchy completions of partial metric spaces under symmetric denseness. They asked if every (non-empty) partial metric space $X$ has a p-Cauchy completion $\bar{ X}$ such that $X$ is dense but not symmetrically dense in $\bar{ X}$. 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.
Categories: math.GN