Remarks on Fixed Point Assertions in Digital Topology, 2

TL;DR

This paper critically examines fixed point theorems in digital topology, highlighting that many recent results obtained by mimicking classical topology tools are often incorrect, trivial, or limited in scope.

Contribution

It provides a critical analysis showing the limitations and inaccuracies of applying classical topology methods to digital topology fixed point results.

Findings

Many recent fixed point results are incorrect or trivial

Classical topology tools may not be suitable for digital topology

The paper clarifies limitations in current digital topology fixed point research

Abstract

Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces. We show that in many cases, researchers using these tools have derived conclusions that are incorrect, trivial, or limited.