A self-similar set with non-locally connected components
General Topology
2024-04-01 v1
Abstract
Luo, Rao and Xiong [Topol. Appl. 322 (2022), 108271] conjectured that if a planar self-similar iterated function system with the open set condition does not involve rotations or reflections, then every connected component of the attractor is locally connected. We create a homogeneous counterexample of Lalley-Gatzouras type, which disproves this conjecture.
Cite
@article{arxiv.2403.19999,
title = {A self-similar set with non-locally connected components},
author = {Jian-Ci Xiao},
journal= {arXiv preprint arXiv:2403.19999},
year = {2024}
}
Comments
6 pages, 1 figure