Unicoherence at subcontinua
type: Item
instance of: scholarly article
title: Unicoherence at subcontinua
zbMATH Open document ID: 0589.54043
DOI: 10.1016/0166-8641(86)90005-2
published in: Topology and its Applications
publication date: 1986-01-01T00:00:00Z
review text: The author introduces a localized notion of unicoherence: a metric continuum X is unicoherent at a subcontinuum Y provided if A and B are proper subcontinua of X and \(X=A\cup B\) then \(A\cap B\cap Y\) is connected. General results are obtained and used to characterize two other forms of unicoherence. In particular, it is shown that strong unicoherence [defined by Bennett] is equivalent to unicoherence at every subcontinuum and weak hereditary unicoherence [defined by Maćkowiak] is equivalent to unicoherence at every subcontinuum with nonempty interior. Strong unicoherence and weak hereditary unicoherence are proved equivalent for continua in which each indecomposable subcontinuum has nonempty interior. Finally, several characterizations of dendrites are obtained.
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54F55
Mathematics Subject Classification ID: 54F50
zbMATH DE Number: 3947186
zbMATH Keywords: aposyndesis
zbMATH Keywords: strong unicoherence
zbMATH Keywords: unicoherence at every subcontinuum
zbMATH Keywords: weak hereditary unicoherence
zbMATH Keywords: dendrites
author: Margaret Ann Owens
reviewed by: Lewis Lum
MaRDI profile type: Publication
full work available at URL: 0166-8641(86)90005-2
OpenAlex ID: W2062590067
cites work: Aposyndetic properties of unicoherent continua
cites work: Aposyndetic Continua and Certain Boundary Problems
cites work: Q3304890
cites work: Q4108942
cites work: Q4185474
description: scientific article; zbMATH DE number 3947186