摘要
本文主要证明了欧氏平面上,面积不超过某给定正数的紧凸集全体,赋予Hausdorff度量拓扑构成的超空间,是一个AR;还证明了[0,1]×[0,1]中,Lebesgue测度不超过某正数m_0(m_0<1)的紧凸集全体同胚于Hilbert方体Q=[-1,1]~ω.
In this paper,we mainly proved that the hyperspace of all compact convex sets which not exceeding a given positive constant,endowed with the Hausdorff metric topology,is homeomorphic to an AR; And also proved that the hyperspace of all compact convex sets which Lebesgue measure not exceeding m_0( m_0<1) in[0,1]×[0,1],is homeomorphic to the Hilbert cube Q =[-1,1]~ω.
出处
《南京师大学报（自然科学版）》
CAS
CSCD
北大核心
2017年第4期12-15,共4页
Journal of Nanjing Normal University(Natural Science Edition)
基金
国家自然科学基金(11471202)
陕西省教育厅基金(16JK1183)
