Finitely fibered Rosenthal compacta and trees

We study some topological properties of trees with the interval topology. In particular, we characterize trees which admit a 2-fibered compactification and we present two examples of trees whose one-point compactifications are Rosenthal compact with certain renorming properties of their spaces of continuous functions.

💡 Research Summary

The paper investigates topological and functional‑analytic properties of trees equipped with the interval topology, focusing on two intertwined themes: (i) the existence of low‑dimensional fibered compactifications, and (ii) the Rosenthal compactness of one‑point compactifications together with special renorming phenomena in the associated spaces of continuous functions.
The authors begin by recalling the interval topology on a tree (T): for each node the basic open sets consist of the “up‑set” and “down‑set” relative to that node, which yields a finer topology than the usual order topology and captures the branching structure in a natural way.
A central notion introduced is that of an (n)-fibered compactification. A compact space (K) is said to be (n)-fibered if there exists a continuous surjection (f:K\to