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The cantor set and inverse limits of upper semi-continuous functions

被引：0
|
作者：
Capulin, Felix [1 ]
del Portal, Francisco R. Ruiz [2 ]
Sanchez-Garrido, Monica [1 ]
机构：
[1] Univ Autonoma Estado Mexico, Fac Ciencias, Dept Math, Inst Literario 100, Toluca 50000, Estado De Mexic, Mexico
[2] Univ Complutense Madrid, Dept Algebra Geometria & Topol, Madrid, Spain
来源：
BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA | 2024年 / 30卷 / 03期
关键词：
Inverse limits; Upper semi-continuous functions; Cantor set; BONDING FUNCTIONS; GRAPHS;
D O I：
10.1007/s40590-024-00651-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study inverse limits with a single upper semi-continuous function F such that it is the union of mappings defined from a compact metric space X into itself. We prove that if Dom(F) is a totally disconnected space, then (sic) (X,F) is homeomorphic to the Cantor set. This gives a partial answer to a problem posed by Ingram (Topol Appl 299:1-11, 2021), and it answers a question asked by Capulin et al. (Topol Proc 60:71-80, 2022).
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页数：12
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