Fans having unique cones
type: Item
instance of: scholarly article
title: Fans having unique cones
zbMATH Open document ID: 1473.54030
author: Alejandro Illanes
author: Daria Michalik
author: Verónica Martínez-de-la-Vega
published in: Topology and its Applications
publication date: 2021-09-27T00:00:00Z
review text: A continuum is a compact connected nondegenerate metric space. We say that a continuum \(X\) has unique cone provided that the following property holds: if \(Y\) is a continuum and \(cone(X)\) is homeomorphic to \(cone(Y)\), then \(X\) is homeomorphic to \(Y\). Now, a fan is an arcwise continuum with exactly one ramification point having the property that the intersection of any two subcontinua is connected. In [Topol. Proc. 52, 35--43 (2018; Zbl 1409.54011)], \textit{D. Michalik} proved the following result: Theorem. Let us assume that \(X\) and \(Y\) are locally connected curves not being ANRs. Then \(cone(X)\) and \(cone(Y)\) are homeomorphic if and only if \(X\) is homeomorphic to \(Y\). The objective of this paper under review is to prove that a fan has unique cone if and only if it is not the cone over a zero-dimensional non-degenerate compact metric space.
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54B15
Mathematics Subject Classification ID: 54F50
zbMATH DE Number: 7401497
zbMATH Keywords: continuum
zbMATH Keywords: cone
zbMATH Keywords: dendrite
zbMATH Keywords: fan
reviewed by: Alicia Santiago-Santos
MaRDI profile type: Publication
full work available at URL: j.topol.2020.107511
OpenAlex ID: W3112080192
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DOI: 10.1016/J.TOPOL.2020.107511
description: scientific article; zbMATH DE number 7401497