Meshed continua have unique second and third symmetric products

被引：9

作者：

Guerrero-Mendez, Luis A. ^{[1
]}

Herrera-Carrasco, David ^{[1
]}

Lopez, Maria de J. ^{[1
]}

Macias-Romero, Fernando ^{[1
]}

机构：

[1] Benemerita Univ Autonoma Puebla, Fac Ciencias Fis Matemat, Puebla 72570, Pue, Mexico

来源：

TOPOLOGY AND ITS APPLICATIONS | 2015年 / 191卷

关键词：

Almost meshed; Continuum; Dendrite; Hyperspace; Local dendrite; Meshed; Peano continuum; Unique hyperspace; FINITE GRAPHS; DENDRITES; HYPERSPACES; RIGIDITY;

D O I：

10.1016/j.topol.2015.04.018

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 a positive integer n, we consider the n-th symmetric product F-n (X) with the Hausdorff metric. In this paper we prove that if X is a meshed continuum, Y is a continuum and F-n(X) is homeomorphic to F-n(Y), then X is homeomorphic to Y, for each n is an element of {2,3}. This answers a question by Alejandro Illanes. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：16 / 27

页数：12

共 25 条

[1] Acosta G, 2002, LECT NOTES PURE APPL, V230, P33
[2] Local dendrites with unique hyperspace C(X)
Acosta, Gerardo
Herrera-Carrasco, David
Macias-Romero, Fernando
[J]. TOPOLOGY AND ITS APPLICATIONS, 2010, 157 (13) : 2069 - 2085
[3] Acosta G, 2009, HOUSTON J MATH, V35, P451
[4] DENDRITES AND SYMMETRIC PRODUCTS
Acosta, Gerardo
Hernandez-Gutierrez, Rodrigo
Martinez-de-la-Vega, Veronica
[J]. GLASNIK MATEMATICKI, 2009, 44 (01) : 195 - 210
[5] [Anonymous], 1999, MONOGRAPHS TXB PURE
[6] Finite graphs have unique symmetric products
Castañeda, E
Illanes, A
[J]. TOPOLOGY AND ITS APPLICATIONS, 2006, 153 (09) : 1434 - 1450
[7] Local connectedness in hyperspaces
Charatonik, Janusz J.
Illanes, Alejandro
[J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2006, 36 (03) : 811 - 856
[8] Duda R., 1968, Fundam. Math., V62, P265
[9] Dugundji J., 1978, Allyn and Bacon Series in Advanced Mathematics
[10] RIGIDITY OF HYPERSPACES
Hernandez-Gutierrez, Rodrigo
Illanes, Alejandro
Martinez-de-la-Vega, Veronica
[J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2015, 45 (01) : 213 - 236

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