On Multi Metric Space
Project no. 23913 · Status: Kapanmış · 2022
Summary
<p>This project mainly consistof four chapters.</p><p>In the first chapter, the project topic is introduced and some related works are given.</p><p>In the second chapter, some basic definitions and theorems are mentioned for easy understanding of the thesis by readers.</p><p>In the third chapter, Das and Roy in 2021 introduced the notion of a multi-metric space (ç_metric) over a multiset defined on a set. Also, the concepts of multi topology, multi open and closed sets are defined by the same researchers are given.</p><p>In the last part of the project, with the help of the definition of multi metric space, the concept of generalized multi metric space (multi_G_metric) is defined and its basic properties are studied. A multi-G_topology generated with the help of the multi_G_metric is given and its Fundamentals features are investigated. Then with the help of these concepts the definitions of multi G_convergence and multi G_Cauchy sequence are given and some of their properties are analyzed.</p>