Hosseini, A., Fosner, A. (2019). On the Structure of Metric-like Spaces. Sahand Communications in Mathematical Analysis, 14(1), 159-171. doi: 10.22130/scma.2018.74393.316

Amin Hosseini; Ajda Fosner. "On the Structure of Metric-like Spaces". Sahand Communications in Mathematical Analysis, 14, 1, 2019, 159-171. doi: 10.22130/scma.2018.74393.316

Hosseini, A., Fosner, A. (2019). 'On the Structure of Metric-like Spaces', Sahand Communications in Mathematical Analysis, 14(1), pp. 159-171. doi: 10.22130/scma.2018.74393.316

Hosseini, A., Fosner, A. On the Structure of Metric-like Spaces. Sahand Communications in Mathematical Analysis, 2019; 14(1): 159-171. doi: 10.22130/scma.2018.74393.316

^{1}Department of Mathematics, Kashmar Higher Education Institute, Kashmar, Iran.

^{2}University of Primorska, Cankarjeva 5, SI-6000 Koper, Slovenia.

Abstract

The 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.

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