Lelek's problem is not a metric problem

TL;DR

This paper demonstrates that Lelek's problem regarding the chainability of continua with span zero is fundamentally non-metric, showing that non-metric counterexamples can be transformed into metric ones.

Contribution

It reveals that Lelek's problem is not inherently metric, providing a method to convert non-metric counterexamples into metric ones.

Findings

Non-metric counterexamples can be transformed into metric ones.

Lelek's problem is not a metric problem.

The problem's nature is fundamentally non-metric.

Abstract

We show that Lelek's problem on the chainability of continua with span zero is not a metric problem: from a non-metric counterexample one can construct a metric one.