Factorization of Bijections onto Ordered Spaces

TL;DR

This paper studies how continuous bijections from zero-dimensional spaces onto certain ordered subspaces can be factored through zero-dimensional subspaces of ordered spaces with controlled weight, revealing structural insights.

Contribution

It introduces a class of subspaces of ordered spaces where such factorizations are always possible, extending understanding of the structure of ordered spaces and continuous bijections.

Findings

Continuous bijections from zero-dimensional spaces can be factored through zero-dimensional subspaces of ordered spaces.

The factorization preserves the weight of the target space.

The results apply to a specific class of subspaces of ordered spaces.

Abstract

We identify a class of subspaces of ordered spaces $\mathcal L$ for which the following statement holds: If $f:X\to L\in \mathcal L$ is a continuous bijections of a zero-dimensional space $X$, then $f$ can be re-routed via a zero-dimensional subspace of an ordered space that has weight not exceeding that of $L$.