A self-similar set with non-locally connected components

Autor:	Xiao, Jian-Ci
Rok vydání:	2024
Předmět:	Mathematics - General Topology Primary 28A80 Secondary 54D05
Druh dokumentu:	Working Paper
Popis:	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. Comment: 6 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.19999 Zobrazit plný text záznamu View this record from Arxiv