Complete Closedness of Maximal Monotone Operators

(This paper is dedicated to the memory of Professor Kwan Chao-Chin, former academic member and director of the Institute of System Science of the Academy of Chinese Sciences.) A maximal monotone operator in R_n is completely closed, i.e., not only closed for points, but also closed for directions. Such a completely closed operator is locally bounded at a point if and only if it is bounded at that point.