The complexity of the classification problems of finite-dimensional continua

被引：2
|
作者：
Chang, Cheng [1 ]
Gao, Su [2 ]
机构：
[1] Mercy Coll, Sch Liberal Arts, 555 Broadway, Dobbs Ferry, NY 10522 USA
[2] Univ North Texas, Dept Math, 1155 Union Circle 311430, Denton, TX 76203 USA
来源：
TOPOLOGY AND ITS APPLICATIONS | 2019年 / 267卷
关键词：
Continuum; Path-component; Borel reducible; Graph isomorphism;
D O I：
10.1016/j.topol.2019.106876
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the homeomorphic classification of finite-dimensional continua as well as several related equivalence relations. We show that, when n >= 2, the classification problem of n-dimensional continua is strictly more complex than the isomorphism problem of countable graphs. We also obtain results that compare the relative complexity of various equivalence relations. (C) 2019 Elsevier B.V. All rights reserved.
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页数：18
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