Topological fractals revisited

Benjamin Vejnar; Kl\'ara Karasov\'a

Topological fractals revisited

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arxiv 2209.15394 v2 pith:ZRUBZWBR submitted 2022-09-30 math.GN math.DS

Klára Karasová , Benjamin Vejnar This is my paper · ORCID

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keywords topologicalfractalanswersconjecturecontinuumdiscusseveryextends

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We prove that every Peano continuum with uncountably many local cut points is a topological fractal. This extends some recent results and it partially answers a conjecture by Hata. We also discuss the number of mappings which are necessary for witnessing the structure of a topological fractal.

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Cantor subsystems on the Gehman dendrite
math.DS 2024-11 conditional novelty 8.0 of 10

Every surjective Cantor dynamical system is conjugate to the endpoint subsystem of a mixing map on the Gehman dendrite, and the authors claim the same for exact maps.

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