On the 0-Cauchy Completion of A Partial Metric Space

Authors : Seithuti Philemon Moshokoa

Pages : 10-15

View : 14 | Download : 17

Publication Date : 2016-07-13

Article Type : Research Paper

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