[0,1] is not a Minimality Detector for [0,1]^2

TL;DR

The paper demonstrates that a sequence in [0,1]^2 can be non-minimal yet still produce minimal sequences under any continuous transformation, challenging assumptions about minimality detection.

Contribution

It introduces a counterexample sequence in [0,1]^2 that defies minimality detection by continuous functions, revealing limitations in existing minimality criteria.

Findings

Existence of a non-minimal sequence in [0,1]^2

Such sequence yields minimal sequences under all continuous maps

Challenges assumptions about minimality detection methods

Abstract

This paper shows that there exists a non-minimal sequence $\bar{x} \in ([0,1]^2)^{\mathbb{N}}$ such that for any continuous function $f:[0,1]^2 \to [0,1]$, the sequence obtained by mapping terms of $\bar{x}$ by $f$ is minimal.