Topological developments of $\mathcal{F}$-metric spaces

TL;DR

This paper explores the topological properties of $\

Contribution

It establishes fundamental topological properties of $\\mathcal{F}$-metric spaces and introduces fixed point results for specific contractive mappings.

Findings

$\\mathcal{F}$-metric spaces are Hausdorff and first countable.

Separable $\\mathcal{F}$-metric spaces are second countable.

Fixed point results for altering distance functions and Kannan-type mappings.

Abstract

In this manuscript, we claim that the newly introduced $\mathcal{F}$-metric spaces are Hausdorff and also first countable. Moreover, we assert that every separable $\mathcal{F}$-metric space is second countable. Additionally, we acquire some interesting fixed point results concerning altering distance functions for contractive-type mappings and Kannan-type contractive mappings in this exciting context. However, most of the findings are well-furnished by several non-trivial numerical examples. Finally, we raise an open problem regarding the metrizability of such kind of spaces.