An existence theorem of maximum points for a set preordered (not necessarily partial ordered) by a convex cone of a real linear space is presented. The proof of the theorem is different from the usual technic, that is the separation theorem, as used in Khazayel and Farajzadeh (Optim Lett 15:847–858, 2021) and Araya (Appl Math Lett 22:501–504, 2009). The main result of this gives an affirmative answer to the open problem was raised by Corley (J Optim Theory Appl 31(2):277–281, 1980) and also this paper can be viewed as a new version of the main theorem appeared in the above papers with mild assumptions and without using the separation theory and the notions of the topological interior or algebraic.

提出了由实线性空间的凸锥预先排序（不一定是部分排序）的集合的最大点的存在定理。该定理的证明与通常的技术不同，即分离定理，如 Khazayel 和 Farajzadeh (Optim Lett 15:847–858, 2021) 和 Araya (Appl Math Lett 22:501–504, 2009) 中使用的。主要结果对 Corley 提出的开放问题给出了肯定的答案（J Optim Theory Appl 31(2):277–281, 1980），并且这篇论文可以被视为主要定理的新版本上述论文带有温和的假设，没有使用分离理论和拓扑内部或代数的概念。