# New examples of non-commutative Valdivia compact spaces

## TL;DR

This paper characterizes certain trees with coarse wedge topology to identify new examples of non-commutative Valdivia compact spaces that are not Valdivia, expanding the understanding of these topological structures.

## Contribution

It provides a characterization of trees with coarse wedge topology that admit a retractional skeleton, leading to new examples of non-commutative Valdivia compact spaces.

## Key findings

- Identified conditions for trees with coarse wedge topology to have a retractional skeleton
- Constructed new examples of non-commutative Valdivia compact spaces
- Showed these spaces are not Valdivia

## Abstract

The aim of this note is to characterize trees, endowed with coarse wedge topology, that have a retractional skeleton. We use this characterization to provide new examples of non-commutative Valdivia compact spaces that are not Valdivia.