• METRIZABILITY OF COMPLEX VALUED METRIC SPACES AND SOME REMARKS ON FIXED POINT THEOREMS IN COMPLEX VALUED METRIC SPACES

Abstract

We discuss on a topological question in complex valued metric spaces, namely metrizability. We prove that every complex valued metric space is metrizable and hence complex valued metric spaces are not real generalizations of metric spaces. We also show that some of the fixed point theorems recently generalized to complex valued metric spaces are consequences of their counter parts in the setting of metric spaces and hence are redundant.