Existence of quasi-arcs

TL;DR

This paper proves that doubling, linearly connected metric spaces are quasi-arc connected, providing a new, concise proof of Tukia's theorem, which advances understanding of the structure of such spaces.

Contribution

It offers a new, shorter proof of Tukia's theorem demonstrating quasi-arc connectivity in doubling, linearly connected metric spaces.

Findings

Doubling, linearly connected metric spaces are quasi-arc connected

Provides a new proof of Tukia's theorem

Simplifies understanding of metric space connectivity

Abstract

We show that doubling, linearly connected metric spaces are quasi-arc connected. This gives a new and short proof of a theorem of Tukia.