Centers and shore points of a dendroid
type: Item
instance of: scholarly article
title: Centers and shore points of a dendroid
zbMATH Open document ID: 1119.54027
author: Van Nall
published in: Topology and its Applications
publication date: 2007-06-26T00:00:00Z
review text: A dendroid is an hereditarily unicoherent arc connected continuum. A subcontinuum of a dendroid is a bottleneck if it intersects every arc connecting two nonempty open sets in the dendroid. In 2003, P. Minc proved that every dendroid contains a point, called the center of the dendroid, that is contained in arbitrarily small bottlenecks. If the point is itself a bottleneck then that point is called a strong center. Shore points have been used to study the hyperspace structure of dendroids. In this paper author studies the relationship between center points and shore points in a dendroid. It is shown that if a dendroid contains a strong center, then any finite union of the arc components of the set of shore points is a shore set.
Mathematics Subject Classification ID: 54F55
Mathematics Subject Classification ID: 54F15
zbMATH DE Number: 5167616
zbMATH Keywords: dendroid
zbMATH Keywords: shore point
zbMATH Keywords: center point
zbMATH Keywords: continuum
reviewed by: Shou Lin
MaRDI profile type: Publication
full work available at URL: j.topol.2006.01.019
OpenAlex ID: W2075640571
cites work: Centers of a dendroid
cites work: Finite unions of shore sets
cites work: Bottlenecks in dendroids
cites work: Shore points in dendroids and conical pointed hyperspaces
cites work: Q4004123
cites work: Q4064159
cites work: Q3888161
DOI: 10.1016/J.TOPOL.2006.01.019
description: scientific article; zbMATH DE number 5167616