From the text: Nicholas Yannelis pointed out that Theorem 2 on p. 164 of [ibid. 14, No. 2–3, 163–165 (1984; Zbl 1273.91178)] is not correct. It is indeed true that some additional hypothesis is needed. We show that the theorem is valid if \(X\) is assumed to be a convex subset. This is the only additional assumption needed. In particular, it is not necessary to assume that \(X\) is closed. We reformulate the theorem in an infinite-dimensional setting. The proof given below is essentially the same as the one given in the paper. In fact, it is somewhat simpler.