R^P中有界凸集的几个性质

Some Properties on the Convex Set in R￣p

在Ｒ￣Ｐ中，给定一个有界凸集Ｂ，给定一个点，则存在一个在Ｘ支撑Ｂ的超平面，本文限定，且Ｘ是Ｂ的极大元，从而讨论这时的支撑超平面的性质，并由此得出了Ｘ是有界凸集Ｂ的极大元的充要条件。

Giving a bounded convex set B in Rp,a point X e∈B.Then there exists ahyperplane that supports B at X. In this paper,we discussed the properties of the sup- porting hyperplane when X∈B and X is a maximum element of B. From which we get anecessary and sufficient condition for X be a maximum element of the bounded convexset B.