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).

引用

页数：12

共 50 条

[1] Inverse limits of upper semi-continuous functions, connectedness and the Cantor set
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[J]. TOPOLOGY AND ITS APPLICATIONS, 2021, 303
[2] Inverse limits of upper semi-continuous set valued functions
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[6] INVERSE LIMITS OF UPPER SEMI-CONTINUOUS FUNCTIONS THAT ARE UNIONS OF MAPPINGS
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[8] UPPER SEMI-CONTINUOUS SET-VALUED FUNCTIONS
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[J]. ACTA MATHEMATICA, 1982, 149 (1-2) : 87 - 125
[9] Categories of inverse systems of compacta with upper semi-continuous bonding functions
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[J]. TOPOLOGY AND ITS APPLICATIONS, 2016, 204 : 23 - 40
[10] Computability on continuous, lower semi-continuous and upper semi-continuous real functions
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[J]. THEORETICAL COMPUTER SCIENCE, 2000, 234 (1-2) : 109 - 133

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