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Fractal Necklaces With No Cut Points

Author

Listed:
  • FAN WEN

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

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.

Suggested Citation

  • Fan Wen, 2022. "Fractal Necklaces With No Cut Points," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-9, June.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:04:n:s0218348x22500918
    DOI: 10.1142/S0218348X22500918
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