The structure of Whitney blocks

被引：2

作者：

Elena Aguilera, Maria ^{[1
]}

Illanes, Alejandro ^{[2
]}

机构：

[1] Ctr Bachillerato Tecnol Ind & Serv 94, Periodista Roberto Pita Cornejo 17, Patzcuaro 61607, Mich, Mexico

[2] Univ Nacl Autonoma Mexico, Inst Matemat, Cd Univ, Mexico City 04510, DF, Mexico

来源：

TOPOLOGY AND ITS APPLICATIONS | 2016年 / 206卷

关键词：

Arc; Arc-like; Circle-like; Continuum; Hyperspace; Simple closed curve; Simple triod; Whitney block; Whitney level; Whitney map;

D O I：

10.1016/j.topol.2016.03.015

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 subcontinua of X. A Whitney block is a set of the form mu(-1)([s,t]), where mu : C(X) -> [0, 1] is a Whitney map and 0 <= s < t < 1. In this paper we study continua for which Whitney blocks are homeomorphic to X x [0, 1]. We characterize an arc, a simple closed curve and simple n-ods in terms of Whitney blocks. We also show that if X is arc-like, then each Whitney block for C(X) is 2-cell-like; and if X is circle-like, then each Whitney block of the form mu(-1)([0, t]) is ring-like. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：215 / 227

页数：13