A self-similar set with non-locally connected components

Jian-Ci Xiao

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arXiv · 2403.19999

A self-similar set with non-locally connected components

Jian-Ci Xiao

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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.

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Jian-Ci Xiao. 2024-03-29. A self-similar set with non-locally connected components. https://arxiv.org/abs/2403.19999

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