Sahand Communications in Mathematical Analysis (Apr 2019)

On the Structure of Metric-like Spaces

  • Amin Hosseini,
  • Ajda Fosner

DOI
https://doi.org/10.22130/scma.2018.74393.316
Journal volume & issue
Vol. 14, no. 1
pp. 159 – 171

Abstract

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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.

Keywords