Homeomorphisms of the Pseudoarc
General Topology
2024-12-31 v1 Dynamical Systems
Logic
Abstract
We construct homeomorphisms of compacta from relations between finite graphs representing their open covers. Applied to the pseudoarc, this yields simple Fra\"iss\'e theoretic proofs of several important results, both old and new. Specifically, we recover Bing's classic results on the uniqueness and homogeneity of the pseudoarc. We also show that the autohomeomorphism group of the pseudoarc has a dense conjugacy class, thus confirming a conjecture of Kwiatkowska.
Cite
@article{arxiv.2412.20401,
title = {Homeomorphisms of the Pseudoarc},
author = {Tristan Bice and Maciej Malicki},
journal= {arXiv preprint arXiv:2412.20401},
year = {2024}
}