On compact trees with the coarse wedge topology

TL;DR

This paper studies compact trees with the coarse wedge topology, characterizing Valdivia compact trees, analyzing continuous function spaces, and establishing properties like property (M) and Plichko-ness for certain trees.

Contribution

It provides a structural description of Valdivia compact trees and characterizes the continuous function spaces on these trees, advancing understanding in non-separable Banach space theory.

Findings

Valdivia compact trees characterized by inner structures

All compact trees possess property (M)

Function spaces on trees with height less than ω₁·ω₀ are Plichko

Abstract

In the present paper we investigate the class of compact trees, endowed with the coarse wedge topology, in the area of non-separable Banach spaces. We describe Valdivia compact trees in terms of inner structures and we characterize the space of continuous functions on them. We prove that all compact trees have the property $(M)$. Finally we prove that the space of continuous functions on an arbitrary tree with height less than $\omega_1\cdot\omega_0$ is Plichko.