关于局部双序凸空间与超有效点

On the Locally Biorder-convex Spaces and Super Efficiency

论文引入一类新的空间概念：局部双序凸空间，讨论了双序拓扑线性空间为局部双序凸空间的一系列充要条件，证明了局部双序凸空间中每一个连续线性泛函均能分解为两个单调连续线性泛函之差，并得到一个超有效点的存在性结果.

In this paper, we introduce the concept of the biorder-convex space, and provide some necessary and sufficient conditions for a topological linear space to be locally biorder-convex. Furthermore, we prove a biordering positive decomposition theorem. As an interesting application of the results in this paper, we discuss the existence of super efficiency.