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A self-similar set with non-locally connected components
- Publication Year :
- 2024
-
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.<br />Comment: 6 pages, 1 figure
- Subjects :
- Mathematics - General Topology
Primary 28A80, Secondary 54D05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2403.19999
- Document Type :
- Working Paper