Ultrametrizable spaces are homeomorphic to clade spaces of pruned trees

2024/07/31 by Itamar Bellaïche, Bellaïche, Itamar
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Topology and Set Theory #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2407.21763

Abstract

This paper demonstrates that every ultrametric space is homeomorphic to a clade space of a pruned tree, i.e., a subspace of a tree's canopy. Furthermore, it characterizes several topological properties of ultrametrizable spaces through the features of their representing trees. This approach suggests that topological properties of ultrametrizable spaces should be studies via the study of naturally ordered pruned trees.

Related

• Labeled trees generating complete, compact, and discrete ultrametric spaces
• Extremal properties and morphisms of finite ultrametric spaces and their representing trees
• Totally bounded ultrametric spaces and locally finite trees
• Isomorphism of trees and isometry of ultrametric spaces
• Labeled Trees Generating Separable and Locally Finite Ultrametrics