FRACTAL NECKLACES WITH NO CUT POINTS

Fan Wen ()
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Fan Wen: College of Mathematics, School of Science and Engineering, University of Tsukuba, Ibaraki 305-8575, Japan

FRACTALS (fractals), 2022, vol. 30, issue 04, 1-9

Abstract: The fractal necklaces in ℠d (d ≥ 2) introduced in this paper are a class of connected fractal sets generated by the so-called necklace IFSs, for which a lot of basic topology questions are interesting. We give two subclasses of fractal necklaces and prove that every necklace in these two classes has no cut points. Also, we prove that every stable self-similar necklace in ℠2 has no cut points, whilst an analog for self-affine necklaces is false.

Keywords: Fractal Necklace; Stability; Bounded Ramification; Cut Point; Open Set Condition (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:30:y:2022:i:04:n:s0218348x22500918

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DOI: 10.1142/S0218348X22500918

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