Introducing $n$-sequences and study of their topological properties

Document Type : Research Paper

Authors

1 Department of Applied Mathematics, Zakir Husain College of Engineering and Technology, Aligarh Muslim University, Aligarh-202002, India

2 Department of Basic Engineering Sciences, Engineering Faculty, Malatya Turgut Ozal University, Malatya-44040, Turkey

Abstract

In this article, the concept of $n$-sequences in topological spaces has been introduced which is new to the existing literature. We study the sequential limit aspect of statistical convergence for such sequences. Besides, the notions of subsequences, limit points, statistical limits points, and statistical cluster points in topological spaces have been given for $n$-sequences. This material contains a detailed explanation of inclusion relations between these points spaces and their basic properties. We also introduce $s_{n}$ and $s_{n}^{*}$-convergent spaces and discuss some of their properties.

Keywords

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Volume 13, Issue 2
July 2022
Pages 2389-2398
  • Receive Date: 01 May 2021
  • Revise Date: 11 August 2021
  • Accept Date: 21 August 2021