THE EXISTENCE AND UNIQUENESS OF COMPLETION OF COMPLEX VALUED METRIC SPACES

Abstract

Completion of a metric space has been investigated and proved its existence and uniqueness. While a complex valued metric space is considered as a generalization of a metric space, we study the completion properties of complex valued metric spaces. Using redefined definitions of isometry and denseness in complex valued metric spaces which correspond to the definitions in metric spaces, we prove the existence and uniqueness of completion of a complex valued metric space.