A self-similar set with non-locally connected components
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911819011981312 |
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| author | Xiao, Jian-Ci |
| author_facet | Xiao, Jian-Ci |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19999 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A self-similar set with non-locally connected components Xiao, Jian-Ci General Topology Primary 28A80, Secondary 54D05 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. |
| title | A self-similar set with non-locally connected components |
| topic | General Topology Primary 28A80, Secondary 54D05 |
| url | https://arxiv.org/abs/2403.19999 |