Generalized Kuratowski Closure Operators in the Bipolar Metric Setting

Abstract

We initiate the investigation of the topological aspects of bipolar metric spaces. In this context, some concepts that generalize open and closed balls and sets, accumulation points, closure and interior operators for bipolar metric spaces, of which little is known about their topological behaviors, are discussed. In addition, some essential properties regarding these notions were obtained, and counterexamples were provided for some expected but not satisfied properties.