Towards Strong Convergence and Cauchy Sequences in Binary Metric Spaces

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Publication Details

Author list: Yadav, Shubham; Gopal, Dhananjay; Chaipunya, Parin; Martínez-Moreno, Juan;

Publisher: MDPI

Publication year: 2022

Volume number: 11

Issue number: 8

ISSN: 2075-1680

eISSN: 2075-1680

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85137319430&doi=10.3390%2faxioms11080383&partnerID=40&md5=2dcd4b5e29efa33c3218b42ba0bb4077

Languages: English-Great Britain (EN-GB)

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Abstract

A Kuratowski topology is a topology specified in terms of closed sets rather than open sets. Recently, the binary metric was introduced as a symmetric, distributive-lattice-ordered magma-valued function of two variables satisfying a “triangle inequality” and subsequently proved that every Kuratowski topology can be induced by such a binary metric. In this paper, we define the strong convergence of a sequence in a binary metric space and prove that strong convergence implies convergence. We state the conditions under which strong convergence is equivalent to convergence. We define a strongly Cauchy sequence and a strong complete binary metric space. Finally, we give the strong completion of all binary metric spaces with a countable indexing set. © 2022 by the authors.

Keywords

binary metric, convergence in binary metric, generalized metric