Restricting open surjections

TL;DR

The paper proves that continuous open surjections between complete metric spaces can be restricted to domains with the same density character as the target, refining previous results in the field.

Contribution

It improves a recent theorem by showing such restrictions are always possible, enhancing understanding of the structure of open surjections between metric spaces.

Findings

Any continuous open surjection from a complete metric space can be restricted to match the density character of the target.

The result refines previous theorems by Aron, Jaramillo, and Le Donne.

The theorem applies to a broad class of metric spaces, including complete ones.

Abstract

We show that any continuous open surjection from a complete metric space to another metric space can be restricted to a surjection for which the domain has the same density character as the target. This improves a recent result of Aron, Jaramillo and Le Donne.