Remarks on Fixed Point Assertions in Digital Topology, 5

TL;DR

This paper critically examines existing claims about fixed points in digital metric spaces, highlighting errors, incorrect proofs, or trivial results, to clarify the validity of such assertions.

Contribution

It identifies and clarifies inaccuracies and trivialities in previous fixed point assertions within digital topology.

Findings

Several published fixed point assertions are incorrect or trivial.

Some proofs in digital topology literature are flawed or incomplete.

The paper clarifies the correct understanding of fixed points in digital metric spaces.

Abstract

We discuss published assertions concerning fixed points in digital metric spaces that are incorrect or incorrectly proven, or reduce to triviality.