Geodesic
A criterion for self-similar sets to be totally disconnected
Jun Luo1 ; Dong Hong Xiong2
1Chongqing University, College of Mathematics and Statistics
2Chongqing Business Vocational College, Department of Public Administration
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 1155-1159
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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.  
Keywords: Totally disconnected, self-similar set, finite type, E-connected family

Jun Luo  1   ; Dong Hong Xiong  2

1 Chongqing University, College of Mathematics and Statistics
2 Chongqing Business Vocational College, Department of Public Administration 
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Jun Luo; Dong Hong Xiong. A criterion for self-similar sets to be totally disconnected. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 1155-1159. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a31/