Remarks on unicoherence at subcontinua
type: Item
instance of: scholarly article
title: Remarks on unicoherence at subcontinua
zbMATH Open document ID: 0929.54024
author: Włodzimierz J. Charatonik
author: Alejandro Illanes
author: Janusz J. Charatonik
published in: Tsukuba Journal of Mathematics
publication date: 2000-01-25T00:00:00Z
review text: The authors provide examples showing that some of the results in the paper [\textit{Zhou Youcheng}, Tsukuba J. Math. 20, No. 2, 257-262 (1996; Zbl 0883.54029)] are incorrect. While other assertions from that paper are true, their proofs contain essential gaps so expanded arguments are provided. The main result in Zhou Youcheng's paper asserted that a locally connected continuum, \(X\), is unicoherent at a subcontinuum \(Y\) if and only if \(X\) has property (b) at \(Y\). In this paper, the authors demonstrate that equivalence does not hold and provide an expanded proof that the unicoherence of \(X\) at \(Y\) is sufficient for \(X\) to have property (b) at \(Y\).
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54F55
zbMATH DE Number: 1309322
zbMATH Keywords: locally connected continuum
zbMATH Keywords: unicoherence
zbMATH Keywords: property (b)
reviewed by: Donald E. Bennett
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496163668
OpenAlex ID: W1691236157
DOI: 10.21099/TKBJM/1496163668
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description: scientific article; zbMATH DE number 1309322