A criterion for self-similar sets to be totally disconnected

Författare

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

Nyckelord:

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.

 

Nedladdningar

Publicerad

2021-09-16

Nummer

Vol 46 Nr 2 (2021)

Sektion

Articles

Licens

Copyright (c) 2021 The Finnish Mathematical Society

Creative Commons-licens

Detta verk är licensierat under en Creative Commons Erkännande-IckeKommersiell 4.0 Internationell-licens.

Referera så här

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