On compact trees with the coarse wedge topology
Jacopo Somaglia

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 . Finally we prove that the space of continuous functions on an arbitrary tree with height less than is Plichko.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
