Topological fractals revisited

TL;DR

This paper proves that certain complex topological spaces called Peano continua with many local cut points are topological fractals, extending recent results and addressing a conjecture by Hata, while also analyzing the mappings needed to demonstrate fractal structure.

Contribution

It establishes that Peano continua with uncountably many local cut points are topological fractals, extending previous work and partially resolving Hata's conjecture.

Findings

Peano continua with uncountably many local cut points are topological fractals

Extended recent results in topological fractal theory

Discussed the number of mappings needed to witness fractal structure

Abstract

We prove that every Peano continuum with uncountably many local cut points is a topological fractal. This extends some recent results and it partially answers a conjecture by Hata. We also discuss the number of mappings which are necessary for witnessing the structure of a topological fractal.