|Table of Contents|

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 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)
Keywords:
hyperspacecompact convex setLebesgue 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:

[1] CURTIS D W. Hyperspaces of noncompact metric spaces[J]. Compositio Math,1980,40(2):139-152.
[2]CURTIS D W,SCHORI R M. Hyperspaces of polyhedra are Hilbert cubes[J]. Fund Math,1978,99(3):189-197.
[3]SCHORI R M,WEST J E. Hyperspaces of graphsare Hilbert cubes[J]. Pacific J Math,1974,53(2):239-251.[4]SCHORI R M,WEST J E. Hyperspaces of the closed unit interval is a Hilbert cube[J]. Trans Amer Math Soc,1975,213(1):217-235.[5]NADLER S,QUINN J E,STAVROKAS N M. Hyperspaces of compact convex sets[J]. Pacific J of Math,1979,83:411-462.[6]MONTEJANO L. The hyperspace of compact convex subsets of an open subset of . Bull Pol Acad Sci Math,1987,35(11/12):793-799.[7]BANAKH T,HETMAN I. A“hidden”characterization of polyhedral convex sets[J]. Studia Math,2011,206:63-74.[8]BANAKH T,HETMAN I,SAKAI K. Recognizing the topology of the space of closed convex subsets of a Banach space[J]. Studia Math,2013,216(1):17-33.[9]BANAKH T,KURIHARA M,SAKAI K. Hyperspaces of normed linear spaces with the Attouch-Wets topology[J]. Set-Valued Anal,2003,11(1):21-36.[10]SAKAI K. The spaces of compact convex sets and bounded closed convex sets in a Banach space[J]. Houston J Math,2008,34(1):289-300.[11]SAKAI K,YAGUCHI M. Hyperspaces of Banach spaces with the Attouch-Wets topology[J]. Set-Valued Anal,2004,12(3):329-344.[12]SAKAI K,YANG Z Q. The spaces of closed convex sets in Euclidean spaces with the Fell topology[J]. Bull Pol Acad Sci Math,2007,55(2):139-143.[13]YANG Z,HU S,WEI G. The topological structure of continuous function space of non-compact space with the Fell topology[J]. Topology Proc,2013(41):17-38.[14]YANG Z,WU N. A topological position of the set of continuous maps in the set of upper semicontinuous maps[J]. Sci China Ser A,Math,2009(52):1 815-1 828.[15]YANG Z,YAN P,Topological classification of function spaces with the Fell topology Ⅰ[J]. Topology Appl,2004(178):146-159.[16]YANG Z,ZHENG Y,CHEN J. Topological classification of function spaces with the Fell topology Ⅱ[J]. Topology Appl,2015,187(1):82-96.[17]YANG Z,ZHENG Y,CHEN L. Topological classification of function spaces with the Fell topology Ⅲ[J]. Topology Appl,2016(197):112-132.[18]YANG Z,ZHANG B. The hyperspace of the hypographs of continuous maps with the Fell topology[J]. Acta mathematica sinica,english series,2012(28):57-66.[19]YANG Z,ZHOU X. A pair of spaces of upper semi-continuous maps and continuous maps[J]. Topology Appl,2007(154):1 737-1 747.[20]BAZILEVICH L E. On the hyperspace of strictly convex bodies[J]. Matem Studi,1993,2:83-86.[21]BAZILEVICH L E. Topology of the hyperspace of convex bodies of constant width[J]. Mathematical notes,1997,62(6):813-819.[22]杨鎏. 定面积的紧凸体的超空间的拓扑结构[J]. 南京大学学报(自然科学版),2016,52(3):558-565.[23]MILL J V. Infinite-dimensional topology of function spaces[M]. Amsterdam:North-Holland Math Library 64,Elsevier Sci Publ B V,2001.[24]ENGELKING R. General topology[M]. 2nd ed. Berlin:Heldermann Verlag,1989.

Memo

Memo:
-
Last Update: 2017-12-30