[1]杨 鎏,杨寒彪.与Lebesgue测度有关的紧凸集的超空间的拓扑结构[J].南京师范大学学报(自然科学版),2017,40(04):12.[doi:10.3969/j.issn.1001-4616.2017.04.003]
 Yang Liu,Yang Hanbiao.The Topological Structures of Hyperspaces of CompactConvex Sets Concerned with Lebesgue Measure[J].Journal of Nanjing Normal University(Natural Science Edition),2017,40(04):12.[doi:10.3969/j.issn.1001-4616.2017.04.003]
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与Lebesgue测度有关的紧凸集的超空间的拓扑结构()
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第40卷
期数:
2017年04期
页码:
12
栏目:
·数学与计算机科学·
出版日期:
2017-12-30

文章信息/Info

Title:
The Topological Structures of Hyperspaces of CompactConvex Sets Concerned with Lebesgue Measure
文章编号:
1001-4616(2017)04-0012-04
作者:
杨 鎏1杨寒彪2
(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)
Author(s):
Yang Liu1Yang Hanbiao2
(1.Department of Mathematics,Shaanxi Xueqian Normal University,Xi’an 710100,China)(2.School of Mathematics and Computational Science,Wuyi University,Jiangmen 529099,China)
关键词:
超空间紧凸集Lebesgue测度
Keywords:
hyperspacecompact convex setLebesgue measure
分类号:
O189.1
DOI:
10.3969/j.issn.1001-4616.2017.04.003
文献标志码:
A
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m0(m0<1)的紧凸集全体同胚于Hilbert方体Q=[-1,1]ω.
Abstract:
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 m0(m0<1)in[0,1]×[0,1],is homeomorphic to the Hilbert cube Q=[-1,1]ω.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2017-04-14.
基金项目:国家自然科学基金(11471202)、陕西省教育厅基金(16JK1183).
通讯联系人:杨鎏,博士,讲师,研究方向:拓扑学,泛函分析,算子理论. E-mail:381900567@qq.com
更新日期/Last Update: 2017-12-30