A criterion for self-similar sets to be totally disconnected

Authors

  • Jun Luo Chongqing University, College of Mathematics and Statistics
  • Dong Hong Xiong Chongqing Business Vocational College, Department of Public Administration

Keywords:

Totally disconnected, self-similar set, finite type, E-connected family

Abstract

In this paper, we prove that, under Bandt's finite type condition, a self-similar set is totally disconnected if and only if the \(E\)-connected families on every level are uniformly finite.

 

Issue
Vol. 46 No. 2 (2021)
Section
Articles

Published

2021-09-16

How to Cite

Luo, J., & Xiong, D. H. (2021). A criterion for self-similar sets to be totally disconnected. Annales Fennici Mathematici, 46(2), 1155–1159. Retrieved from https://afm.journal.fi/article/view/111296

Copyright (c) 2021 The Finnish Mathematical Society

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