Making holes in hyperspaces

被引：10
作者：
Anaya, Jose G. [1 ]
机构：
[1] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico
来源：
TOPOLOGY AND ITS APPLICATIONS | 2007年 / 154卷 / 10期
关键词：
continuum; hyperspaces; property (b); unicoherence;
D O I：
10.1016/j.topol.2006.09.017
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let X be a metric continuum and C(X) the hyperspace of all nonempty subcontinua of X. Let A epsilon C(X), A is said to make a hole in C(X), if C(X) - {A} is not unicoherent. In this paper we study the following problem. Problem: For which A epsilon C(X), A makes a hole in C(X). In this paper we present some partial solutions to this problem in the following cases: (1) A is a free arc; (2) A is a one-point set; (3) A is a free simple closed curve; (4) A = X. (C) 2007 Elsevier B.V. All rights reserved.
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页码：2000 / 2008
页数：9
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