Remarks on unicoherence at subcontinua (Q1293146)

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 \(Y\).