与Lebesgue测度有关的紧凸集的超空间的拓扑结构  

The Topological Structures of Hyperspaces of Compact Convex Sets Concerned with Lebesgue Measure

作　　者：杨鎏[1] 杨寒彪 

机构地区：[1]陕西学前师范学院数学系,陕西西安710100 [2]五邑大学数学与计算机科学学院,广东江门529099

出　　处：《南京师大学报（自然科学版）》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)

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.

关 键 词：超空间 紧凸集 LEBESGUE测度 

分 类 号：O189.1[理学—数学]