The continuum self-similar tree

TL;DR

This paper introduces the continuum self-similar tree (CSST), characterizes its topology, and applies these results to the continuum random tree (CRT), providing new insights into the topological structure of various self-similar trees.

Contribution

The paper defines the CSST, characterizes its topology, and answers a question about the CRT's topology, extending understanding of self-similar trees.

Findings

Characterization of the topological structure of the CSST

Topological description of the CRT answering Curien's question

Extension to trees with various branch point valences

Abstract

We introduce the continuum self-similar tree (CSST) and characterize it topologically. We apply this to answer a question of Curien about the topology of the continuum random tree (CRT). We also give a topological characterization of other trees with branch points of finite or infinite valences.