A comment to Matkowski's paper (Q390808)

In [Topology Appl. 160, No.~3, 524--531 (2013; Zbl 1263.47067)], \textit{J. Matkowski} referred to \textit{L. Pasicki} [Czech. Math. J. 61, No.~2, 383--388 (2011; Zbl 1249.46011)] for the proof of Lemma~3, which was, however, presented in a generality not to be found in the given reference and hence requiring separate proof. Here, the author supplies that proof and also makes precise how Matkowski's subsequent Theorem~3 follows from said Lemma.