On the complex valued metric-like spaces

Abstract

The main purpose of this paper is to study complex valued metric-like spaces as an extension of metric-like spaces, complex valued partial metric spaces, partial metric spaces, complex valued metric spaces and metric spaces. In this article, the concepts such as quasi-equal points, completely separate points, convergence of a sequence, Cauchy sequence, cluster points and complex diameter of a set are defined in a complex valued metric-like space. Moreover, this paper is an attempt to present compatibility definitions for the complex distance between a point and a subset of a complex valued metric-like space and also for the complex distance between two subsets of a complex valued metric-like space. In addition, the topological properties of this space are also investigated.