Metric spaces with discrete topological fundamental group
It was asserted in Theorem 5.1 [\textit{D. K. Biss}, Topology Appl. 124, No. 3, 355--371 (2002; Zbl 1016.57002)] that the topological fundamental group \(\pi_1^{\text{top}}(X,p)\) of a metric space is discrete if and only if \(X\) is semilocally simply connected. In this brief note, the author gives a counterexample to this theorem and fixes it by adding the condition of locally path connectedness on \(X\).
scientific article; zbMATH DE number 5121456