南京大学学报(自然科学版) ›› 2016, Vol. 52 ›› Issue (3): 558–.

• • 上一篇    

定面积的紧凸体的超空间的拓扑结构

 杨 鎏   

  • 出版日期:2016-07-03 发布日期:2016-07-03
  • 作者简介: 汕头大学理学院数学系,汕头,515063
  • 基金资助:
     国家自然科学基金(11471202)

 The topological structure of hyperspace of compact convex bodies of constant area

 Yang Liu   

  • Online:2016-07-03 Published:2016-07-03
  • About author: Department of Mathematics,Shantou University,Shantou,515063,China

摘要:  主要研究了具有某种几何性质的紧凸体的超空间的拓扑结构.实际上证明了:欧氏平面?2上面积为正数v0的紧凸体全体,赋予Hausdorff度量拓扑所构成的超空间,是一个Q­流形其中Q表示赋予乘积拓扑的Hilbert方体[-1,1]ω.

Abstract:  In this note,we mainly study the topological structure of hyperspace of compact convexbodies with some geometric property.In fact,we have proved that the hyperspace of all compact convex bodies of constant area in Euclidean plane ?2 with the Hausdorff metric topology is homeomorphic to a Q­manifold,where Q is the Hilbert cube [-1,1]ω endowed with the product topology.

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