Aronszajn Compacta

TL;DR

This paper investigates a special class of compact spaces where the structure of continuous maps onto metric compacta forms an Aronszajn tree of closed subsets, revealing new insights into their topological properties.

Contribution

It introduces and analyzes the concept of Aronszajn compacta, connecting topological properties with tree structures of closed subsets.

Findings

Identification of conditions characterizing Aronszajn compacta

Establishment of the relationship between compacta and Aronszajn trees

New topological properties derived from the tree structure

Abstract

We consider a class of compacta X such that the maps from X onto metric compacta define an Aronszajn tree of closed subsets of X.