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The Topological Structures of Hyperspaces of CompactConvex Sets Concerned with Lebesgue Measure(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2017年04期
Page:
12-
Research Field:
·数学与计算机科学·
Publishing date:

Info

Title:
The Topological Structures of Hyperspaces of CompactConvex Sets Concerned with Lebesgue Measure
Author(s):
Yang Liu1; Yang 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)
Keywords:
hyperspace; compact convex set; Lebesgue measure
PACS:
O189.1
DOI:
10.3969/j.issn.1001-4616.2017.04.003
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.

References:

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Last Update: 2017-12-30