On the 0-Cauchy Completion of A Partial Metric Space

Year 2016, Volume: 4 , 10 - 15, 13.07.2016

Seithuti Philemon Moshokoa

Abstract

It is well known that every metric space admits a Cauchy completion which is unique up to isometry. This result was extended to partial metric spaces, which are generalization of metric spaces. It is the purpose of this paper to construct a 0-Cauchy completion of a partial metric space and we shall show that a 0-Cauchy completion is unique up to isometry. Finally, it is observed that the 0-Cauchy completion of a partial metric space is smaller than its Cauchy completion but coincides with the classical Cauchy completion when restricted to the category of metric spaces.

Keywords

Partial metric space, complete, completion

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