In page 1975 of [W. Roth, A uniform boundedness theorem for locally convex cones, Proc. Amer. Math. Soc. 126 (1998), no. 7, 1973–1982] we can see: In a locally convex vector space $E$ a barrel is defined to be an absolutely convex closed and absorbing subset A of E. The set $U = {(a, b) \in E^2: a − b \in A} then is seen to be a barrel in the sense of Roth’s definition. With a counterexample, we show that it is not enough for U to be a barrel in the sense of Roth’s definition. Then we correct this error with providing its converse and an application.