  Locally convex cones are generalization of locally convex spaces. The
assertion, whether a barreled cone is an upper-barreled cone or not, was posed
as a question in [A. Ranjbari, H. Saiflu, Projective and inductive limits in
locally convex cones, J. Math. Anal. Appl. 332 (2) (2007) 1097-1108]. In this
paper, we show that a barreled locally convex cone is not necessarily
upper-barreled.
