Universal mappings with fixed range in $\mathbb R^n$
Volume 181 / 2026
Colloquium Mathematicum 181 (2026), 197-208
MSC: Primary 54B99; Secondary 54C05, 54C10, 54C25
DOI: 10.4064/cm9604-10-2025
Published online: 30 September 2026
Abstract
We prove the existence of universal elements in classes of continuous and semi-open mappings having the same range $Y$. Our study is based on the so-called saturated classes of topological spaces. Based on this result, we also prove the existence of universal elements in the class ${\rm C}^{{\rm sop}}({\mathbb E}, \mathbb {R}^n)$ of all continuous and semi-open mappings with domains in a saturated class ${\mathbb E}$ of topological spaces and range $\mathbb {R}^n$. We apply our results to various saturated classes ${\mathbb E}$.
