The Existence And Application Of The Minimal Generaling Set Of A Convey Set

This paper mainly resolves partly the open problem whether there is a unique smallest subset for a convex set whose convex hull is equal to the set , which was proposed by Steven R.Lay in the material Convex Sets and Their Application. The paper provides and proves a sufficient and necessary condition about the open problem . Moreover the paper prove the answer is negative for an open set in En. Meanwhile , the paper discusses how to use the sufficient and necessary condition in practice and gives a conjecture?On the other hand, the paper pay some attention to the economical application of the convex set 's smallest generating set .It covers from the productive enterprise to the vender till to the consumer. Based on the dynamic convex smallest generating set , how the enterprise and the vender obtain the greatest benefits, how the consumer gear the idea of consumption.