Parovicenko spaces with structures

TL;DR

This paper explores an analogue of the Parovicenko property within structured categories of compact spaces, providing an internal characterization specifically for compact median spaces.

Contribution

It introduces a new analogue of the Parovicenko property and characterizes it internally in the context of compact median spaces.

Findings

Established an internal characterization of the property in median spaces

Extended the Parovicenko property to structured categories of compact spaces

Provided insights into the structure of compact median spaces

Abstract

We study an analogue of the Parovicenko property in categories of compact spaces with additional structures. In particular, we present an internal characterization of this property in the class of compact median spaces.