# A Revisit to n-Normed Spaces through Its Quotient Spaces

## TL;DR

This paper investigates properties of n-normed spaces via their quotient spaces, establishing equivalences of continuity types and proving a fixed point theorem for contractive mappings.

## Contribution

It introduces a new approach to analyze n-normed spaces through quotient spaces, including fixed point results for contractive mappings.

## Key findings

- All types of continuity are equivalent in this context
- A fixed point theorem for contractive mappings is established
- Properties of n-normed spaces are characterized via quotient space norms

## Abstract

In this paper, we study some features of n-normed spaces with respect to norms of its quotient spaces. We define continuous functions with respect to the norms of its quotient spaces and show that all types of continuity are equivalent. We also study contractive mappings on n- normed spaces using the same approach. In particular, we prove a fixed point theorem for contractive mappings on a closed and bounded set in an n-normed space.