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中文摘要：
本简报指出：若是部凸空间中存在一个凸锥它既具紧基，又具非空内部，则该局部凸空间必为有限维的．利用局部凸空间的对偶理论，在不对序锥附近加其他条件的前提下，我们获得了Benson真有效点的对偶特征．由此，我们给出了几乎锥次凸状集值映照的向量优化问题的Benson真极小元的标量化定理．
英文摘要：
In this brief report, it is pointed out that if a locally convex space has a convex cone with a compact base and with a nonempty interior, then it is finite dimensional. By using the dual theory of locally convex spaces, we obtain a dual characterization for Benson proper efficient points without any additional assumption on the ordering cone. From this we give a scalarization theorem for Benson proper minimizers of vector optimization problems with nearly cone-subconvexlike set-valued maps.
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