University of MaraghehSahand Communications in Mathematical Analysis2322-580714120190401On the Structure of Metric-like Spaces1591713489510.22130/scma.2018.74393.316ENAminHosseiniDepartment of Mathematics, Kashmar Higher Education Institute, Kashmar, Iran.AjdaFosnerUniversity of Primorska, Cankarjeva 5, SI-6000 Koper, Slovenia.Journal Article20171031The main purpose of this paper is to introduce several concepts of the metric-like spaces. For instance, we define concepts such as equal-like points, cluster points and completely separate points. Furthermore, this paper is an attempt to present compatibility definitions for the distance between a point and a subset of a metric-like space and also for the distance between two subsets of a metric-like space. In this study, we define the diameter of a subset of a metric-like space, and then we provide a definition for bounded subsets of a metric-like space. In line with the aforementioned issues, various examples are provided to better understand this space.http://scma.maragheh.ac.ir/article_34895_b50d85dc44f99ed205ebcea9caa64428.pdf