On the topology of n-normed spaces with respect to norms of its quotient spaces

TL;DR

This paper explores the topological properties of n-normed spaces by introducing quotient space norms, providing new insights into convergence, closedness, boundedness, and completeness within these spaces.

Contribution

It introduces a novel approach using quotient space norms to analyze the topology of n-normed spaces, offering fresh perspectives on their structure.

Findings

Characterization of convergence sequences using quotient norms

Identification of closed and bounded sets via quotient norms

Assessment of completeness in n-normed spaces

Abstract

In this paper, we study some topological characteristics of the n-normed spaces. We observe convergence sequences, closed sets, and bounded sets in the n-normed spaces using norms of quotient spaces that will be constructed. These norms will be a new viewpoint in observing the characteristics of the n-normed spaces. By using these norms, we also review the completeness of the n-normed spaces.