具有β-中点性质的非β-凸集(0<β<1)  

The Sets with β-Midpoint Property but no β-Convexity(0<β<1)

作　　者：王见勇[1] 

机构地区：[1]常熟理工学院数学系,江苏常熟215500

出　　处：《数学的实践与认识》2016年第11期267-271,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11471236)

摘　　要：首先给出具有中点性质1/2x+1/2y∈A,x,y∈A的开集或者闭集均是凸集的完整证明,接着通过给出满足β-中点性质1/(2^(1/β))x+1/(2^(1/β))y∈A,x,y∈A(0<β<1),但非β-凸集的开集与闭集的例子各一个,从中点性质是否蕴涵相应凸性的角度揭示了集合的β-凸性与通常凸性之间的另一显著差异.In this paper, we first prove that for open sets and closed sets, the midpoint property 1/2x＋1/2y∈ A, x,y∈ A implies the convexity, and then construct an open set and a closed set with β-midpoint property but no β-convexity （0 〈 β〈 1）, that show another significant difference between β-convexity and convexity.

关 键 词：β-凸集 局部Β-凸空间 (β-)中点性质 

分 类 号：O174.13[理学—数学]