In [1], we performed a systematic investigation of reparametrizations of continuous paths in a Hausdorff space that relies crucially on a proper understanding of stop data of a (weakly increasing) reparametrization of the unit interval. I am indebted to Marco Grandis (Genova) for pointing out tome that the proof of Proposition 3.7 in [1] iswrong. Fortunately, the statment of that Proposition and the results depending on it stay correct. It is the purpose of this note to provide correct proofs.
[1] U. Fahrenberg and M. Raussen, Reparametrizations of continuous paths, J. Homotopy Relat. Struct. 2 (2007), no. 2, 93-117.