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Fractal necklaces with no cut points

Authors :
Wen, Fan
Publication Year :
2021

Abstract

The fractal necklaces in R^d (d>1) 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 R^2 has no cut points, whilst an analog for self-affine necklaces is false.

Subjects

Subjects :
Mathematics - General Topology

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2105.00407
Document Type :
Working Paper
Full Text :
https://doi.org/10.1142/S0218348X22500918